Question

How many ounces of a 25% alcohol solution and a 38% alcohol solution must be combined to obtain 39 ounces of a 32% solution

Answer 1

Answer:

18 ounces of the 25% solution

21 ounces of the 38% solution

Step-by-step explanation:

let a be the ounces of 25% alcohol solution

let b be the ounces of 38% alcohol solution

a + b = 39

0.25a + 0.38b = 0.32(39) = 12.48

Rearrange a + b = 39:

a = 39 - b

Now we can substitute a = 39 - b into the other equation

0.25a + 0.38b = 12.48

0.25(39 - b) + 0.38b = 12.48

Simplify by distributing

9.75 - 0.25b + 0.38b = 12.48

Collect like terms

9.75 + 0.13b = 12.48

Isolate b to solve

0.13b = 2.73

b = 2.73/0.13

b = 21

Sub b = 21 into an equation to find "a"

a + b = 39

a + 21 = 39

a = 39 - 21

a = 18

Therefore we need 18 ounces of the 25% solution and 21 ounces of the 38% solution.