SOLUTION: Austin thought he was supposed to mix 3 cans of frozen juice to every five cans of water. Madeline thought you mixed four cans of water to every one can of frozen juice. The real r

Question 933630: Austin thought he was supposed to mix 3 cans of frozen juice to every five cans of water. Madeline thought you mixed four cans of water to every one can of frozen juice. The real recipe calls for 3 cans of water to every one can of frozen juice. Show how much of Austin's mixture and how much of Madeline's mixture is needed to make the correct juice recipe.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Austin's mixture is 3/(3+5)=3/8 frozen juice
Madeline's mixture is 1/(1+4)=1/5 frozen juice
The real recipe is 1/(1+3)=1/4 frozen juice
Let x=amount of Austin's mixture needed
Let y=amount of Madeline's mixture needed
Now we know that the amount of pure frozen juice that exists before the mixture takes place ((3/8)x+(1/5)y) has to equal the amount of frozen juice in the final mixture ((1/4)(x+y)). Soooo our equation is:
(3/8)x +(1/5)y=(1/4)(x+y) multiply each term by 40
15x+8y=10x+10y
5x=2y
x=(2/5)y
So, for every 5 gal of Madeline's mixture, we need (2/5)*5=2 gal of Austin's mixture
CK
Let's say Madeline used 40 gal, then Austin would need to use(2/5)*40=16 gal
(3/8)*16+(1/5)*40=(1/4)*56
6+8=14
14=14
Hope this helps---ptaylor
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