Respuesta :
Step
The question involve a direct proportion because when quantity inrease, the other increase.
Concept:
Find the constant of proportionality by dividing one quantity by the other.
Step 2
Find constant of proportionality K for 1/3 cup of pineapple juice for every 3/4 cup of orange juice.
[tex]\begin{gathered} k\text{ = }\frac{1}{3}\text{ }\frac{.}{.}\text{ }\frac{3}{4} \\ k\text{ = }\frac{1}{3}\text{ }\times\text{ }\frac{4}{3} \\ k\text{ = }\frac{4}{9} \end{gathered}[/tex]Step 3
Use can use the direct proportion method
Let P represent the number of cups of pineapple juice
[tex]\begin{gathered} \frac{\frac{1}{3}}{\frac{3}{4}}\text{ = }\frac{P}{3} \\ \text{Cross multiply} \\ \frac{3}{4}P\text{ = }\frac{1}{3}\text{ }\times\text{ 3} \\ \frac{3P}{4}\text{ = 1} \\ 3P\text{ = 4} \\ P\text{ = }\frac{4}{3} \end{gathered}[/tex]Final answer
[tex]\begin{gathered} \frac{4}{3}\text{ cups of pineapple juice is n}eeded\text{ for 3 cups of orange juice.} \\ \frac{4}{3}\text{ cups of Pineapple juice} \end{gathered}[/tex]