Question

calories
20
□
10
90
miles
$\frac{1}{6}$
$\frac{2}{3}$
□
□
the equivalent ratios are $20 : \frac{1}{6}$, $□:\frac{2}{3}$ , $10:\frac{1}{12}$ , and $90:\frac{3}{4}$ .

Explanation:

Step1: Find the constant ratio

First, calculate the calories per mile using the known pair:
$\frac{20}{\frac{1}{6}} = 20 \times 6 = 120$
This means 120 calories are burned per mile.

Step2: Solve for missing calories

Use the constant ratio to find calories for $\frac{2}{3}$ miles:
$\text{Calories} = 120 \times \frac{2}{3} = 80$

Step3: Solve for 10 calories' miles

Rearrange the ratio to find miles for 10 calories:
$\text{Miles} = \frac{10}{120} = \frac{1}{12}$

Step4: Solve for 90 calories' miles

Calculate miles for 90 calories:
$\text{Miles} = \frac{90}{120} = \frac{3}{4}$

Answer:

The missing values are:

• Calories for $\frac{2}{3}$ miles: $80$
• Miles for 10 calories: $\frac{1}{12}$
• Miles for 90 calories: $\frac{3}{4}$

Filled table pairs: $80:\frac{2}{3}$, $10:\frac{1}{12}$, $90:\frac{3}{4}$