Question

a recipe for fruit punch calls for 1 cups of orange juice for every 2 cups of peach juice, and you want to make 48 cups of fruit punch. how many cups of peach juice do you need to make 48 cups of fruit punch? orange juice 16 peach juice 16 16 i need 16 cups of orange juice and \\(\square\\) cups of peach juice.

Explanation:

Step1: Determine the ratio of orange juice to peach juice

The recipe calls for 1 cup of orange juice for every 2 cups of peach juice. So the ratio of orange juice to peach juice is \(1:2\).

Step2: Let the amount of orange juice be \(x\) and peach juice be \(y\)

We know that the total number of cups of fruit punch is 48, so \(x + y=48\). Also, from the ratio, \(y = 2x\).

Step3: Substitute \(y = 2x\) into \(x + y=48\)

We get \(x+2x = 48\), which simplifies to \(3x=48\). Solving for \(x\), we divide both sides by 3: \(x=\frac{48}{3}=16\). This is the amount of orange juice, which matches the given value.

Step4: Find the amount of peach juice

Since \(y = 2x\) and \(x = 16\), then \(y=2\times16 = 32\). We can also see from the diagram that peach juice is represented by two 16 - cup boxes, so \(16 + 16=32\).

Answer:

32