Question

9 use the following situation to answer the questions. six ounces of orange juice contain 75 calories. about how many calories are in fourteen ounces of orange juice? part a write a proportion, make sure to include the units. let x = the number of unknown calories. part b solve for x (b) a 95 calories b 175 calories c 32.14 calories d 112 calories

Explanation:

Step1: Define the proportion

We know that 6 ounces of orange juice has 75 calories. Let \( x \) be the calories in 14 ounces. The proportion is \(\frac{6 \text{ ounces}}{75 \text{ calories}}=\frac{14 \text{ ounces}}{x \text{ calories}}\) (or equivalently \(\frac{75 \text{ calories}}{6 \text{ ounces}}=\frac{x \text{ calories}}{14 \text{ ounces}}\) since the ratio of calories to ounces should be constant).

Step2: Cross - multiply to solve for \( x \)

Using the proportion \(\frac{75}{6}=\frac{x}{14}\), cross - multiplying gives us \( 6x = 75\times14\). First, calculate \( 75\times14=1050\). Then, solve for \( x \) by dividing both sides of the equation \( 6x = 1050\) by 6: \( x=\frac{1050}{6}=175\).

Answer:

B. 175 calories