Question

Apple and cranberry juice are mixed in a ratio of 5 to 3. What amount of each juice would be needed to make a 64-fluid ounce pitcher of apple-cranberry juice?

Answer 1

32

Explanation:

64/2=32

Answer 2

`\text{Apple juice needed: }40\:\mathrm{oz},\\\text{Cranberry juice needed: }24\:\mathrm{oz}`

Explanation:

Let
`a` be the amount of apple juice needed, in ounces. Let
`c` be the amount of cranberry juice needed, in ounces. We can set up the following system of equations:

`\begin{cases}a=(5)/(3)c, \\a+c=64\end{cases}`

Solving, we get:

`(5)/(3)c+c=64,\\\\(8)/(3)c=64,\\\\c=(64\cdot 3)/(8)=\boxed{24\:\mathrm{oz}}`

`a=(5)/(3)c,\\\\a=(5)/(3)(24),\\\\a=\boxed{40\:\mathrm{oz}}`