Question

1. a recipe for sparkling grape juice calls for $1\frac{1}{2}$ quarts of sparkling water and $\frac{3}{4}$ quart of grape juice.

a. how much sparkling water would you need to mix with 9 quarts of grape juice?
b. how much grape juice would you need to mix with $\frac{15}{4}$ quarts of sparkling water?
c. how much of each ingredient would you need to make 100 quarts of punch?

1. a. draw a scaled copy of the circle using a scale factor of 2.

Explanation:

Step1: Find the ratio of sparkling water to grape juice

The ratio of sparkling water to grape juice is \(1\frac{1}{2}:\frac{3}{4}\). Convert \(1\frac{1}{2}\) to \(\frac{3}{2}\). Then the ratio \(\frac{3}{2}:\frac{3}{4}=\frac{\frac{3}{2}}{\frac{3}{4}} = 2:1\)

Step2: Solve part (a)

Since the ratio of sparkling water to grape juice is \(2:1\), if there are \(9\) quarts of grape juice, let the amount of sparkling water be \(x\). Then \(\frac{x}{9}=2\), so \(x = 18\) quarts.

Step3: Solve part (b)

Let the amount of grape juice be \(y\) when there is \(\frac{15}{4}\) quarts of sparkling water. Since the ratio is \(2:1\), \(\frac{\frac{15}{4}}{y}=2\), then \(y=\frac{15}{8}\) quarts.

Step4: Solve part (c)

The total ratio of sparkling water and grape juice is \(2 + 1=3\) parts. For \(100\) quarts of punch, the amount of sparkling water is \(\frac{2}{3}\times100=\frac{200}{3}=66\frac{2}{3}\) quarts and the amount of grape juice is \(\frac{1}{3}\times100=\frac{100}{3}=33\frac{1}{3}\) quarts

Answer:

a. \(18\) quarts
b. \(\frac{15}{8}\) quarts
c. Sparkling water: \(66\frac{2}{3}\) quarts, Grape juice: \(33\frac{1}{3}\) quarts