Answer:
[tex]\text{Apple juice needed: }40\:\mathrm{oz},\\\text{Cranberry juice needed: }24\:\mathrm{oz}[/tex]
Step-by-step explanation:
Let [tex]a[/tex] be the amount of apple juice needed, in ounces. Let [tex]c[/tex] be the amount of cranberry juice needed, in ounces. We can set up the following system of equations:
[tex]\begin{cases}a=\frac{5}{3}c, \\a+c=64\end{cases}[/tex]
Solving, we get:
[tex]\frac{5}{3}c+c=64,\\\\\frac{8}{3}c=64,\\\\c=\frac{64\cdot 3}{8}=\boxed{24\:\mathrm{oz}}[/tex]
[tex]a=\frac{5}{3}c,\\\\a=\frac{5}{3}(24),\\\\a=\boxed{40\:\mathrm{oz}}[/tex]
