SOLUTION: You are making a drink that requires 19 ounces of a 34-proof whiskey. Unfortunately, all you have on hand are 23-proof and 37-proof whiskey. How much of each type of whiskey do you

Question 912694: You are making a drink that requires 19 ounces of a 34-proof whiskey. Unfortunately, all you have on hand are 23-proof and 37-proof whiskey. How much of each type of whiskey do you need to mix to create 19 ounces of a 34-proof whiskey?
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
We need a total of 19 oz. at 34 proof
We want to know how many oz. at 23 proof to mix with 37 proof
a+b=19,
0.23*a+0.37*b=0.34*19
a=19-b
0.23*(19-b)+0.37*b=6.46
4.37-0.23b+0.37*b=6.46
0.14*b=2.09
b=14.9285714
a=19-b
a=4.07142857 oz. at 23 proof
b=14.9285714 oz. at 37 proof
check
0.23*4.07142857+0.37*14.9285714=0.34*19
0.93642857+5.52357143=6.46
6.46=6.46
ok
codemx1
But you say % is half of proof
so we divide by 2
We need a total of 19 oz. at 17%
We want to know how many oz. at 11.5% to mix with 18.5%
a+b=19,
0.115*a+0.185*b=0.17*19
a=19-b
0.115*(19-b)+0.185*b=3.23
2.185-0.115b+0.185*b=3.23
0.07*b=1.045
b=14.9285714
a=19-b
a=4.07142857 oz. at 11.5%
b=14.9285714 oz. at 18.5%
check
0.115*4.07142857+0.185*14.9285714=0.17*19
0.46821429+2.76178571=3.23
3.23=3.23
ok
codemx1
Surprise! It turns out the same.

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