Question

practice: ratios and ratio tablescalories 20 □ 10 90miles $\frac{1}{6}$ $\frac{2}{3}$ □ □the equivalent ratios are $20 : \frac{1}{6}$, $square:\frac{2}{3}$ , $10:square$ , and $square:square$ .

Explanation:

Step1: Find the constant ratio

First, calculate the ratio of calories to miles using the known pair:
$\frac{20}{\frac{1}{6}} = 20 \times 6 = 120$
This means 120 calories per mile, or $\frac{\text{Calories}}{\text{Miles}} = 120$.

Step2: Find missing calories for $\frac{2}{3}$ miles

Multiply miles by the constant ratio:
$120 \times \frac{2}{3} = 80$

Step3: Find missing miles for 10 calories

Divide calories by the constant ratio:
$\frac{10}{120} = \frac{1}{12}$

Step4: Find missing miles for 90 calories

Divide calories by the constant ratio:
$\frac{90}{120} = \frac{3}{4}$

Answer:

The completed ratio table and equivalent ratios are:
Calories: $80$; Miles: $\frac{1}{12}$, $\frac{3}{4}$
Equivalent ratios: $20:\frac{1}{6}$, $80:\frac{2}{3}$, $10:\frac{1}{12}$, and $90:\frac{3}{4}$