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.

b. how does the circumference of the scaled copy compare to the circumference of the original circle?
c. how does the area of the scaled copy compare to the area of the original circle?
student workbook

Explanation:

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

Step2: Solve part a

If the amount of grape juice is \(9\) quarts, and the ratio of sparkling water to grape juice is \(2:1\), then the amount of sparkling water \(x\) satisfies \(\frac{x}{9}=2\). So \(x = 18\) quarts.

Step3: Solve part b

If the amount of sparkling water is \(\frac{15}{4}\) quarts, and the ratio of sparkling water to grape juice is \(2:1\), then let the amount of grape juice be \(y\). We have \(\frac{\frac{15}{4}}{y}=2\), so \(y=\frac{15}{8}\) quarts.

Step4: Solve part c

The total ratio of sparkling water and grape juice is \(2 + 1=3\) parts. If the total amount of punch is \(100\) quarts, then the amount of sparkling water \(s\) is \(\frac{2}{3}\times100=\frac{200}{3}\approx66.67\) quarts and the amount of grape juice \(g\) is \(\frac{1}{3}\times100=\frac{100}{3}\approx33.33\) quarts.

Answer:

a. \(18\) quarts
b. \(\frac{15}{8}\) quarts
c. Approximately \(66.67\) quarts of sparkling water and \(33.33\) quarts of grape juice.