SOLUTION: Vegetable oil which costs $2.10/oz is made by combining soybean oil which costs $2.45/oz with canola oil which costs $1.40/oz. Find the number of oz of soybean oil and canola oil r

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Question 597360: Vegetable oil which costs $2.10/oz is made by combining soybean oil which costs $2.45/oz with canola oil which costs $1.40/oz. Find the number of oz of soybean oil and canola oil required to make 5.1 oz of vegetable oil.
Found 2 solutions by math-vortex, amalm06:
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--
.
[I] Define the variables
s = the amount of soybean oil (in oz.)
c = the amount of canola oil (in oz.)
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[II] Write equations showing the relationships.
There are 5.1 oz. of vegetable oil, so
[amount of soybean oil] + [amount of canola oil] = [amount of vegetable oil]
s%2Bc=5.1
.
The cost of the mixture equals the cost of the ingredients. We get the cost of an oil by multiplying the price for each ounce by the number of ounces in the mixture.
.
[cost of soybean oil in mix] + [cost of canola in mix] = [cost of vegetable oil mixture]
.
An expression for the cost of the soybean oil is 2.45s
An expression for the canola oil is 1.40c
An expression for the vegetable oil is (2.10)*(5.1)
.
2.45s%2B1.40c=%282.10%29%285.1%29
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Simplify.
2.45s%2B1.40c=10.71
.
.
[III] Solve the system of equations
Rewrite the first equation in terms of s.
s%2Bc=5.1
s=5.1-c
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Substitute 5.1-c for s in the second equation.
2.45s%2B1.40c=10.71
2.45%285.1-c%29%2B1.40c=10.71
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Simplify and solve for s.
12.495-2.45c%2B1.40c=10.71
12.495-1.05c=10.71
-1.05c=-1.785
c=1.70
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The equation c = 1.7 means that there are 1.7 oz. of canola oil.
Since there are 5.1 oz. in the mixture, there are 5.1-1.7 = 3.4 oz. of soybean oil.
.
[IV]
Check the oil amounts in the cost equation.
2.45s%2B1.40c=10.71
2.45%283.4%29%2B1.40%281.7%29=10.71
8.33%2B2.38=10.71
10.71=10.71
Bingo!!!
.
That's it. Feel free to email me via gmail if this explanation is unclear.
.
Ms.Figgy
math.in.the.vortex@gmail.com

Vegetable oil which costs $2.10/oz is made by combining soybean oil which costs $2.45/oz with canola oil which costs $1.40/oz. Find the number of oz of soybean oil and canola oil required to make 5.1 oz of vegetable oil.

Answer by amalm06(224) About Me  (Show Source):
You can put this solution on YOUR website!
The problem can be solved quickly and easily using the method of alligation.
Let "c" denote canola oil and "s" denote soybean oil
We will find the ratio of canola oil to soybean oil in 1 oz of the mixture and then use that information to find the amounts of canola oil and soybean oil in 5.1 oz of the mixture
2.10-1.40=0.70
2.45-2.10=0.35
Therefore, C/S=0.35/0.70
Thus, for every 1.05 parts of total mixture, there are 0.35 parts of canola oil
If there are 5.1 oz of total mixture, then the amount of canola oil is
C=(0.35/1.05)(5.1)=1.70 oz (Answer)
S=5.1-1.70=3.40 oz (Answer)