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How much does the fruit concentrate cost in $1$ liter of fruit juice?
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In a factory, $1$ liter of fruit juice contains water cost, fruit concentrate cost and packing cost.
There's fruit concentrate $%25$ of water in the fruit concentrate and water mixture.
Water cost equals $%30$ of fruit concentrate cost.
Packing cost is $0.32$$
If you sell $1$ liter of fruit juice with the price of $2.4$$ which gives $%100$ of profit, How much does the fruit concentrate cost in $1$ liter of fruit juice?
Let's recall $F =$ fruit concentrate cost, $W = $ Water cost and $P= $ packing cost,
$$W + F + underbraceP_0.32 = 1.2$$
Which yields
$$W + F = 0.88$$
Water cost equals $%30$ of fruit concentrate cost.
$$W = dfrac30100F$$
Then we have that
$$F + dfrac30100F = 0.88 implies F = 0.67692$$
I can't think of any way to proceed right now.
Regards!
percentages word-problem
asked Jul 25 at 15:24
Cargobob
368114
 |Â
show 3 more comments
up vote
0
down vote
favorite
In a factory, $1$ liter of fruit juice contains water cost, fruit concentrate cost and packing cost.
There's fruit concentrate $%25$ of water in the fruit concentrate and water mixture.
Water cost equals $%30$ of fruit concentrate cost.
Packing cost is $0.32$$
If you sell $1$ liter of fruit juice with the price of $2.4$$ which gives $%100$ of profit, How much does the fruit concentrate cost in $1$ liter of fruit juice?
Let's recall $F =$ fruit concentrate cost, $W = $ Water cost and $P= $ packing cost,
$$W + F + underbraceP_0.32 = 1.2$$
Which yields
$$W + F = 0.88$$
Water cost equals $%30$ of fruit concentrate cost.
$$W = dfrac30100F$$
Then we have that
$$F + dfrac30100F = 0.88 implies F = 0.67692$$
I can't think of any way to proceed right now.
Regards!
percentages word-problem
asked Jul 25 at 15:24
Cargobob
368114
@saulspatz See the new edit.
– Cargobob
Jul 25 at 15:40
Your first equation is incorrect. On the left-hand side you have the cost of production, and on the right-hand side you have the selling price. We are told that at that price, there is a $100%$ profit, so the right-hand side should be $1.2$
– saulspatz
Jul 25 at 15:44
@saulspatz Too right, let me rewrite those equations.
– Cargobob
Jul 25 at 15:45
First, there's a variable $S$ that appears out of nowhere. That must be a typo for $W$. Second, you aren't using the given that the fruit concentrate mixture is $25%$ water. The statement that water cost is $30%$ of fruit concentrate cost must apply to the unit cost. Try it again.
– saulspatz
Jul 25 at 15:56
@saulspatz I'm truly out of my mind.
– Cargobob
Jul 25 at 16:01
 |Â
show 3 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
In a factory, $1$ liter of fruit juice contains water cost, fruit concentrate cost and packing cost.
There's fruit concentrate $%25$ of water in the fruit concentrate and water mixture.
Water cost equals $%30$ of fruit concentrate cost.
Packing cost is $0.32$$
If you sell $1$ liter of fruit juice with the price of $2.4$$ which gives $%100$ of profit, How much does the fruit concentrate cost in $1$ liter of fruit juice?
Let's recall $F =$ fruit concentrate cost, $W = $ Water cost and $P= $ packing cost,
$$W + F + underbraceP_0.32 = 1.2$$
Which yields
$$W + F = 0.88$$
Water cost equals $%30$ of fruit concentrate cost.
$$W = dfrac30100F$$
Then we have that
$$F + dfrac30100F = 0.88 implies F = 0.67692$$
I can't think of any way to proceed right now.
Regards!
percentages word-problem
asked Jul 25 at 15:24
Cargobob
368114
In a factory, $1$ liter of fruit juice contains water cost, fruit concentrate cost and packing cost.
There's fruit concentrate $%25$ of water in the fruit concentrate and water mixture.
Water cost equals $%30$ of fruit concentrate cost.
Packing cost is $0.32$$
If you sell $1$ liter of fruit juice with the price of $2.4$$ which gives $%100$ of profit, How much does the fruit concentrate cost in $1$ liter of fruit juice?
Let's recall $F =$ fruit concentrate cost, $W = $ Water cost and $P= $ packing cost,
$$W + F + underbraceP_0.32 = 1.2$$
Which yields
$$W + F = 0.88$$
Water cost equals $%30$ of fruit concentrate cost.
$$W = dfrac30100F$$
Then we have that
$$F + dfrac30100F = 0.88 implies F = 0.67692$$
I can't think of any way to proceed right now.
Regards!
percentages word-problem
asked Jul 25 at 15:24
Cargobob
368114
edited Jul 25 at 15:59
asked Jul 25 at 15:24
Cargobob
368114
asked Jul 25 at 15:24
Cargobob
368114
asked Jul 25 at 15:24
Cargobob
368114
368114
@saulspatz See the new edit.
– Cargobob
Jul 25 at 15:40
Your first equation is incorrect. On the left-hand side you have the cost of production, and on the right-hand side you have the selling price. We are told that at that price, there is a $100%$ profit, so the right-hand side should be $1.2$
– saulspatz
Jul 25 at 15:44
@saulspatz Too right, let me rewrite those equations.
– Cargobob
Jul 25 at 15:45
First, there's a variable $S$ that appears out of nowhere. That must be a typo for $W$. Second, you aren't using the given that the fruit concentrate mixture is $25%$ water. The statement that water cost is $30%$ of fruit concentrate cost must apply to the unit cost. Try it again.
– saulspatz
Jul 25 at 15:56
@saulspatz I'm truly out of my mind.
– Cargobob
Jul 25 at 16:01
 |Â
show 3 more comments
@saulspatz See the new edit.
– Cargobob
Jul 25 at 15:40
Your first equation is incorrect. On the left-hand side you have the cost of production, and on the right-hand side you have the selling price. We are told that at that price, there is a $100%$ profit, so the right-hand side should be $1.2$
– saulspatz
Jul 25 at 15:44
@saulspatz Too right, let me rewrite those equations.
– Cargobob
Jul 25 at 15:45
First, there's a variable $S$ that appears out of nowhere. That must be a typo for $W$. Second, you aren't using the given that the fruit concentrate mixture is $25%$ water. The statement that water cost is $30%$ of fruit concentrate cost must apply to the unit cost. Try it again.
– saulspatz
Jul 25 at 15:56
@saulspatz I'm truly out of my mind.
– Cargobob
Jul 25 at 16:01
@saulspatz See the new edit.
– Cargobob
Jul 25 at 15:40
@saulspatz See the new edit.
– Cargobob
Jul 25 at 15:40
Your first equation is incorrect. On the left-hand side you have the cost of production, and on the right-hand side you have the selling price. We are told that at that price, there is a $100%$ profit, so the right-hand side should be $1.2$
– saulspatz
Jul 25 at 15:44
Your first equation is incorrect. On the left-hand side you have the cost of production, and on the right-hand side you have the selling price. We are told that at that price, there is a $100%$ profit, so the right-hand side should be $1.2$
– saulspatz
Jul 25 at 15:44
@saulspatz Too right, let me rewrite those equations.
– Cargobob
Jul 25 at 15:45
@saulspatz Too right, let me rewrite those equations.
– Cargobob
Jul 25 at 15:45
First, there's a variable $S$ that appears out of nowhere. That must be a typo for $W$. Second, you aren't using the given that the fruit concentrate mixture is $25%$ water. The statement that water cost is $30%$ of fruit concentrate cost must apply to the unit cost. Try it again.
– saulspatz
Jul 25 at 15:56
First, there's a variable $S$ that appears out of nowhere. That must be a typo for $W$. Second, you aren't using the given that the fruit concentrate mixture is $25%$ water. The statement that water cost is $30%$ of fruit concentrate cost must apply to the unit cost. Try it again.
– saulspatz
Jul 25 at 15:56
@saulspatz I'm truly out of my mind.
– Cargobob
Jul 25 at 16:01
@saulspatz I'm truly out of my mind.
– Cargobob
Jul 25 at 16:01
 |Â
show 3 more comments
2 Answers
2
active
oldest
votes
up vote
0
down vote
You are correct up to the point where you compute that the cost of the water plus the cost of the fruit concentrate is $88$ cents in a liter of the product.
The sentence "There's fruit concentrate %25 of water in the fruit concentrate and water mixture," is rather awkward. I guess it means that the amount of fruit concentrate in the mixture is $25%$ of the amount of fruit concentrate, or that a liter of the product contains $200$ ml of fruit concentrate and $800$ ml of water.
Let $x$ be the cost of a liter of fruit concentrate. A liter of water costs $30%$ of this or $.3x.$ Since we only have $20%$ of a liter of fruit concentrate in a liter of mixture, the cost of the concentrate is $.2x.$
Also, we have $80%$ of a liter of water, so the cost of the water is $.8(.3x)=.24x$ Then the cost of the concentrate and water in a liter of product is$$
.2x +.24x=.44x$$
Since we've already determined that the cost of the of the water and concentrate is $88$ cents we have $$
.44x=88implies x=200text cents$$
EDIT
I misread the question. I thought we were looking for the cost of a liter of fruit concentrate, but it's actually the cost of the amount of fruit concentrate in a liter of the mixture. That's $20%$ of $200$ cents or $40$ cents.
answered Jul 25 at 16:26
saulspatz
10.4k21323
Can you explain it further?
– Cargobob
Jul 25 at 16:31
@Cargobob Have you decided that the correct answer is not $40$ cents? I'm checking my work.
– saulspatz
Jul 25 at 16:32
The correct answer seems to be $40$ cents.
– Cargobob
Jul 25 at 16:32
See my latest edit.
– saulspatz
Jul 25 at 16:40
However, I truly didn't how you found that equation.
– Cargobob
Jul 25 at 16:40
 |Â
show 2 more comments
up vote
0
down vote
If one liter of juice sells for $$2.40$ at $100%$ profit then the cost is $$1.20$. Subtracting the $$0.32$ cost of packaging, the concentrate and water costs $$0.88$.
The water to concentrate cost ratio in the juice is $1:(frac20%80%cdot frac100%30%) = 1:frac56$ or $6:5$
The water in one liter of juice costs $frac611cdot 0.88 = 48$ cents
The concentrate in one liter of juice costs $frac511cdot 0.88 = 40$ cents
answered Jul 25 at 16:58
Phil H
1,8232311
Can you explain this ratio $1:(frac20%80%cdot frac100%30%) = 1:frac56$?
– Cargobob
Jul 25 at 17:06
For every 1 part cost of water in a mixture, the concentrate cost will be the volume ratio $frac2080$ of concentrate to water times the cost ratio $frac10030$ of concentrate to water. Hence $1 : frac56 = 6 : 5$
– Phil H
Jul 25 at 17:19
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
You are correct up to the point where you compute that the cost of the water plus the cost of the fruit concentrate is $88$ cents in a liter of the product.
The sentence "There's fruit concentrate %25 of water in the fruit concentrate and water mixture," is rather awkward. I guess it means that the amount of fruit concentrate in the mixture is $25%$ of the amount of fruit concentrate, or that a liter of the product contains $200$ ml of fruit concentrate and $800$ ml of water.
Let $x$ be the cost of a liter of fruit concentrate. A liter of water costs $30%$ of this or $.3x.$ Since we only have $20%$ of a liter of fruit concentrate in a liter of mixture, the cost of the concentrate is $.2x.$
Also, we have $80%$ of a liter of water, so the cost of the water is $.8(.3x)=.24x$ Then the cost of the concentrate and water in a liter of product is$$
.2x +.24x=.44x$$
Since we've already determined that the cost of the of the water and concentrate is $88$ cents we have $$
.44x=88implies x=200text cents$$
EDIT
I misread the question. I thought we were looking for the cost of a liter of fruit concentrate, but it's actually the cost of the amount of fruit concentrate in a liter of the mixture. That's $20%$ of $200$ cents or $40$ cents.
answered Jul 25 at 16:26
saulspatz
10.4k21323
Can you explain it further?
– Cargobob
Jul 25 at 16:31
@Cargobob Have you decided that the correct answer is not $40$ cents? I'm checking my work.
– saulspatz
Jul 25 at 16:32
The correct answer seems to be $40$ cents.
– Cargobob
Jul 25 at 16:32
See my latest edit.
– saulspatz
Jul 25 at 16:40
However, I truly didn't how you found that equation.
– Cargobob
Jul 25 at 16:40
 |Â
show 2 more comments
up vote
0
down vote
You are correct up to the point where you compute that the cost of the water plus the cost of the fruit concentrate is $88$ cents in a liter of the product.
The sentence "There's fruit concentrate %25 of water in the fruit concentrate and water mixture," is rather awkward. I guess it means that the amount of fruit concentrate in the mixture is $25%$ of the amount of fruit concentrate, or that a liter of the product contains $200$ ml of fruit concentrate and $800$ ml of water.
Let $x$ be the cost of a liter of fruit concentrate. A liter of water costs $30%$ of this or $.3x.$ Since we only have $20%$ of a liter of fruit concentrate in a liter of mixture, the cost of the concentrate is $.2x.$
Also, we have $80%$ of a liter of water, so the cost of the water is $.8(.3x)=.24x$ Then the cost of the concentrate and water in a liter of product is$$
.2x +.24x=.44x$$
Since we've already determined that the cost of the of the water and concentrate is $88$ cents we have $$
.44x=88implies x=200text cents$$
EDIT
I misread the question. I thought we were looking for the cost of a liter of fruit concentrate, but it's actually the cost of the amount of fruit concentrate in a liter of the mixture. That's $20%$ of $200$ cents or $40$ cents.
answered Jul 25 at 16:26
saulspatz
10.4k21323
Can you explain it further?
– Cargobob
Jul 25 at 16:31
@Cargobob Have you decided that the correct answer is not $40$ cents? I'm checking my work.
– saulspatz
Jul 25 at 16:32
The correct answer seems to be $40$ cents.
– Cargobob
Jul 25 at 16:32
See my latest edit.
– saulspatz
Jul 25 at 16:40
However, I truly didn't how you found that equation.
– Cargobob
Jul 25 at 16:40
 |Â
show 2 more comments
up vote
0
down vote
up vote
0
down vote
You are correct up to the point where you compute that the cost of the water plus the cost of the fruit concentrate is $88$ cents in a liter of the product.
The sentence "There's fruit concentrate %25 of water in the fruit concentrate and water mixture," is rather awkward. I guess it means that the amount of fruit concentrate in the mixture is $25%$ of the amount of fruit concentrate, or that a liter of the product contains $200$ ml of fruit concentrate and $800$ ml of water.
Let $x$ be the cost of a liter of fruit concentrate. A liter of water costs $30%$ of this or $.3x.$ Since we only have $20%$ of a liter of fruit concentrate in a liter of mixture, the cost of the concentrate is $.2x.$
Also, we have $80%$ of a liter of water, so the cost of the water is $.8(.3x)=.24x$ Then the cost of the concentrate and water in a liter of product is$$
.2x +.24x=.44x$$
Since we've already determined that the cost of the of the water and concentrate is $88$ cents we have $$
.44x=88implies x=200text cents$$
EDIT
I misread the question. I thought we were looking for the cost of a liter of fruit concentrate, but it's actually the cost of the amount of fruit concentrate in a liter of the mixture. That's $20%$ of $200$ cents or $40$ cents.
answered Jul 25 at 16:26
saulspatz
10.4k21323
You are correct up to the point where you compute that the cost of the water plus the cost of the fruit concentrate is $88$ cents in a liter of the product.
The sentence "There's fruit concentrate %25 of water in the fruit concentrate and water mixture," is rather awkward. I guess it means that the amount of fruit concentrate in the mixture is $25%$ of the amount of fruit concentrate, or that a liter of the product contains $200$ ml of fruit concentrate and $800$ ml of water.
Let $x$ be the cost of a liter of fruit concentrate. A liter of water costs $30%$ of this or $.3x.$ Since we only have $20%$ of a liter of fruit concentrate in a liter of mixture, the cost of the concentrate is $.2x.$
Also, we have $80%$ of a liter of water, so the cost of the water is $.8(.3x)=.24x$ Then the cost of the concentrate and water in a liter of product is$$
.2x +.24x=.44x$$
Since we've already determined that the cost of the of the water and concentrate is $88$ cents we have $$
.44x=88implies x=200text cents$$
EDIT
I misread the question. I thought we were looking for the cost of a liter of fruit concentrate, but it's actually the cost of the amount of fruit concentrate in a liter of the mixture. That's $20%$ of $200$ cents or $40$ cents.
answered Jul 25 at 16:26
saulspatz
10.4k21323
edited Jul 25 at 16:47
answered Jul 25 at 16:26
saulspatz
10.4k21323
answered Jul 25 at 16:26
saulspatz
10.4k21323
answered Jul 25 at 16:26
saulspatz
10.4k21323
10.4k21323
Can you explain it further?
– Cargobob
Jul 25 at 16:31
@Cargobob Have you decided that the correct answer is not $40$ cents? I'm checking my work.
– saulspatz
Jul 25 at 16:32
The correct answer seems to be $40$ cents.
– Cargobob
Jul 25 at 16:32
See my latest edit.
– saulspatz
Jul 25 at 16:40
However, I truly didn't how you found that equation.
– Cargobob
Jul 25 at 16:40
 |Â
show 2 more comments
Can you explain it further?
– Cargobob
Jul 25 at 16:31
@Cargobob Have you decided that the correct answer is not $40$ cents? I'm checking my work.
– saulspatz
Jul 25 at 16:32
The correct answer seems to be $40$ cents.
– Cargobob
Jul 25 at 16:32
See my latest edit.
– saulspatz
Jul 25 at 16:40
However, I truly didn't how you found that equation.
– Cargobob
Jul 25 at 16:40
Can you explain it further?
– Cargobob
Jul 25 at 16:31
Can you explain it further?
– Cargobob
Jul 25 at 16:31
@Cargobob Have you decided that the correct answer is not $40$ cents? I'm checking my work.
– saulspatz
Jul 25 at 16:32
@Cargobob Have you decided that the correct answer is not $40$ cents? I'm checking my work.
– saulspatz
Jul 25 at 16:32
The correct answer seems to be $40$ cents.
– Cargobob
Jul 25 at 16:32
The correct answer seems to be $40$ cents.
– Cargobob
Jul 25 at 16:32
See my latest edit.
– saulspatz
Jul 25 at 16:40
See my latest edit.
– saulspatz
Jul 25 at 16:40
However, I truly didn't how you found that equation.
– Cargobob
Jul 25 at 16:40
However, I truly didn't how you found that equation.
– Cargobob
Jul 25 at 16:40
 |Â
show 2 more comments
up vote
0
down vote
If one liter of juice sells for $$2.40$ at $100%$ profit then the cost is $$1.20$. Subtracting the $$0.32$ cost of packaging, the concentrate and water costs $$0.88$.
The water to concentrate cost ratio in the juice is $1:(frac20%80%cdot frac100%30%) = 1:frac56$ or $6:5$
The water in one liter of juice costs $frac611cdot 0.88 = 48$ cents
The concentrate in one liter of juice costs $frac511cdot 0.88 = 40$ cents
answered Jul 25 at 16:58
Phil H
1,8232311
Can you explain this ratio $1:(frac20%80%cdot frac100%30%) = 1:frac56$?
– Cargobob
Jul 25 at 17:06
For every 1 part cost of water in a mixture, the concentrate cost will be the volume ratio $frac2080$ of concentrate to water times the cost ratio $frac10030$ of concentrate to water. Hence $1 : frac56 = 6 : 5$
– Phil H
Jul 25 at 17:19
add a comment |Â
up vote
0
down vote
If one liter of juice sells for $$2.40$ at $100%$ profit then the cost is $$1.20$. Subtracting the $$0.32$ cost of packaging, the concentrate and water costs $$0.88$.
The water to concentrate cost ratio in the juice is $1:(frac20%80%cdot frac100%30%) = 1:frac56$ or $6:5$
The water in one liter of juice costs $frac611cdot 0.88 = 48$ cents
The concentrate in one liter of juice costs $frac511cdot 0.88 = 40$ cents
answered Jul 25 at 16:58
Phil H
1,8232311
Can you explain this ratio $1:(frac20%80%cdot frac100%30%) = 1:frac56$?
– Cargobob
Jul 25 at 17:06
For every 1 part cost of water in a mixture, the concentrate cost will be the volume ratio $frac2080$ of concentrate to water times the cost ratio $frac10030$ of concentrate to water. Hence $1 : frac56 = 6 : 5$
– Phil H
Jul 25 at 17:19
add a comment |Â
up vote
0
down vote
up vote
0
down vote
If one liter of juice sells for $$2.40$ at $100%$ profit then the cost is $$1.20$. Subtracting the $$0.32$ cost of packaging, the concentrate and water costs $$0.88$.
The water to concentrate cost ratio in the juice is $1:(frac20%80%cdot frac100%30%) = 1:frac56$ or $6:5$
The water in one liter of juice costs $frac611cdot 0.88 = 48$ cents
The concentrate in one liter of juice costs $frac511cdot 0.88 = 40$ cents
answered Jul 25 at 16:58
Phil H
1,8232311
If one liter of juice sells for $$2.40$ at $100%$ profit then the cost is $$1.20$. Subtracting the $$0.32$ cost of packaging, the concentrate and water costs $$0.88$.
The water to concentrate cost ratio in the juice is $1:(frac20%80%cdot frac100%30%) = 1:frac56$ or $6:5$
The water in one liter of juice costs $frac611cdot 0.88 = 48$ cents
The concentrate in one liter of juice costs $frac511cdot 0.88 = 40$ cents
answered Jul 25 at 16:58
Phil H
1,8232311
answered Jul 25 at 16:58
Phil H
1,8232311
answered Jul 25 at 16:58
Phil H
1,8232311
answered Jul 25 at 16:58
Phil H
1,8232311
1,8232311
Can you explain this ratio $1:(frac20%80%cdot frac100%30%) = 1:frac56$?
– Cargobob
Jul 25 at 17:06
For every 1 part cost of water in a mixture, the concentrate cost will be the volume ratio $frac2080$ of concentrate to water times the cost ratio $frac10030$ of concentrate to water. Hence $1 : frac56 = 6 : 5$
– Phil H
Jul 25 at 17:19
add a comment |Â
Can you explain this ratio $1:(frac20%80%cdot frac100%30%) = 1:frac56$?
– Cargobob
Jul 25 at 17:06
For every 1 part cost of water in a mixture, the concentrate cost will be the volume ratio $frac2080$ of concentrate to water times the cost ratio $frac10030$ of concentrate to water. Hence $1 : frac56 = 6 : 5$
– Phil H
Jul 25 at 17:19
Can you explain this ratio $1:(frac20%80%cdot frac100%30%) = 1:frac56$?
– Cargobob
Jul 25 at 17:06
Can you explain this ratio $1:(frac20%80%cdot frac100%30%) = 1:frac56$?
– Cargobob
Jul 25 at 17:06
For every 1 part cost of water in a mixture, the concentrate cost will be the volume ratio $frac2080$ of concentrate to water times the cost ratio $frac10030$ of concentrate to water. Hence $1 : frac56 = 6 : 5$
– Phil H
Jul 25 at 17:19
For every 1 part cost of water in a mixture, the concentrate cost will be the volume ratio $frac2080$ of concentrate to water times the cost ratio $frac10030$ of concentrate to water. Hence $1 : frac56 = 6 : 5$
– Phil H
Jul 25 at 17:19
add a comment |Â
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@saulspatz See the new edit.
– Cargobob
Jul 25 at 15:40
Your first equation is incorrect. On the left-hand side you have the cost of production, and on the right-hand side you have the selling price. We are told that at that price, there is a $100%$ profit, so the right-hand side should be $1.2$
– saulspatz
Jul 25 at 15:44
@saulspatz Too right, let me rewrite those equations.
– Cargobob
Jul 25 at 15:45
First, there's a variable $S$ that appears out of nowhere. That must be a typo for $W$. Second, you aren't using the given that the fruit concentrate mixture is $25%$ water. The statement that water cost is $30%$ of fruit concentrate cost must apply to the unit cost. Try it again.
– saulspatz
Jul 25 at 15:56
@saulspatz I'm truly out of my mind.
– Cargobob
Jul 25 at 16:01