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{ = }(1)/(3)\text{ }(.)/(.)\text{ }(3)/(4) \\ k\text{ = }(1)/(3)\text{ }*\text{ }(4)/(3) \\ k\text{ = }(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} ((1)/(3))/((3)/(4))\text{ = }(P)/(3) \\ \text{Cross multiply} \\ (3)/(4)P\text{ = }(1)/(3)\text{ }*\text{ 3} \\ (3P)/(4)\text{ = 1} \\ 3P\text{ = 4} \\ P\text{ = }(4)/(3) \end{gathered}`

Final answer

`\begin{gathered} (4)/(3)\text{ cups of pineapple juice is n}eeded\text{ for 3 cups of orange juice.} \\ (4)/(3)\text{ cups of Pineapple juice} \end{gathered}`