To find the unknown distance [tex]\( x \)[/tex] when 3 gallons of gasoline are used, we can use the concept of equivalent ratios. The given problem tells us that a car travels 22 miles for every gallon of gasoline used. Here is the step-by-step solution:
1. Identify the known ratio: We know from the table that the car travels 22 miles for 1 gallon of gasoline.
[tex]\[
\frac{\text{distance}}{\text{gasoline}} = \frac{22 \text{ miles}}{1 \text{ gallon}}
\][/tex]
2. Set up the proportion for the unknown: To find the distance [tex]\( x \)[/tex] when 3 gallons of gasoline are used, we can set up a proportion. Based on the constant ratio we know, we have:
[tex]\[
\frac{22 \text{ miles}}{1 \text{ gallon}} = \frac{x \text{ miles}}{3 \text{ gallons}}
\][/tex]
3. Solve the proportion: To solve for [tex]\( x \)[/tex], we can cross-multiply and then divide.
[tex]\[
22 \text{ miles} \cdot 3 \text{ gallons} = x \text{ miles} \cdot 1 \text{ gallon}
\][/tex]
Simplifying, we get:
[tex]\[
66 = x
\][/tex]
Therefore, the distance [tex]\( x \)[/tex] when 3 gallons of gasoline are used is 66 miles. So, the correct equation showing a pair of equivalent ratios is:
[tex]\[
\frac{22 \text{ miles}}{1 \text{ gallon}} = \frac{66 \text{ miles}}{3 \text{ gallons}}
\][/tex]
This shows that if the car uses 3 gallons of gasoline, it will travel 66 miles.
