Question

find the missing values in the ratio table. then write the equivalent ratios in the order they appear in the table.
calories miles
20 $\frac{1}{6}$
$square$ $\frac{2}{3}$
10 $square$
90 $square$
$square$ : $square$
$square$ : $square$
$square$ : $square$
$square$ : $square$

Explanation:

Step1: Find the unit rate (calories per mile)

From the first row, 20 calories correspond to $\frac{1}{6}$ miles. So the rate is $20\div\frac{1}{6}=20\times6 = 120$ calories per mile.

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

Using the unit rate, calories = $120\times\frac{2}{3}=80$.

Step3: Find miles for 10 calories

Miles = $10\div120=\frac{1}{12}$.

Step4: Find miles for 90 calories

Miles = $90\div120=\frac{3}{4}$.

Step5: Write equivalent ratios

First ratio: $20:\frac{1}{6}$, second: $80:\frac{2}{3}$, third: $10:\frac{1}{12}$, fourth: $90:\frac{3}{4}$.

Answer:

Missing calories for $\frac{2}{3}$ miles: 80; Missing miles for 10 calories: $\frac{1}{12}$; Missing miles for 90 calories: $\frac{3}{4}$; Equivalent ratios: $20:\frac{1}{6}$, $80:\frac{2}{3}$, $10:\frac{1}{12}$, $90:\frac{3}{4}$