Question

Sanjay is making punch. He uses 1/3 cup of pineapple juice for every 3/4 cup of orange juice. How many cups of pineapple juice does he need if he uses 3 cup of orange juice.

Answer 1

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.

$\begin{gathered} k\text{ = }\frac{1}{3}\text{ }\frac{.}{.}\text{ }\frac{3}{4} \\ k\text{ = }\frac{1}{3}\text{ }\times\text{ }\frac{4}{3} \\ k\text{ = }\frac{4}{9} \end{gathered}$

Step 3

Use can use the direct proportion method

Let P represent the number of cups of pineapple juice

$\begin{gathered} \frac{\frac{1}{3}}{\frac{3}{4}}\text{ = }\frac{P}{3} \\ \text{Cross multiply} \\ \frac{3}{4}P\text{ = }\frac{1}{3}\text{ }\times\text{ 3} \\ \frac{3P}{4}\text{ = 1} \\ 3P\text{ = 4} \\ P\text{ = }\frac{4}{3} \end{gathered}$

Final answer

$\begin{gathered} \frac{4}{3}\text{ cups of pineapple juice is n}eeded\text{ for 3 cups of orange juice.} \\ \frac{4}{3}\text{ cups of Pineapple juice} \end{gathered}$