Question

Siri car gets 24 miles per gallon of gas in the city and 32 miles per gallon of gas on the highway. If her car has a 15 gallon gas tank, write a compound inequality to describe the range of distance in miles that her car can travel using a full tank of gas.

Answer 1

The compound inequality to describe the range of distance Siri's car can travel on a full tank of gas is 360 miles ≤ distance ≤ 480 miles, accounting for 24 mpg in the city and 32 mpg on the highway.

Step-by-step explanation:

To find the range of distance Siri's car can travel using a full tank of gas, we need to create a compound inequality that considers both the city and highway miles per gallon (mpg) values. In the city, her car gets 24 mpg, and on the highway, it gets 32 mpg. Using a 15-gallon tank, the minimum distance (all city driving) would be 24 mpg × 15 gallons. The maximum distance (all highway driving) would be 32 mpg × 15 gallons.

The compound inequality representing the range of distances is:

24 mpg × 15 gallons ≤ distance ≤ 32 mpg × 15 gallons

Now, we calculate the distances:

City driving minimum distance: 24 mpg × 15 gallons = 360 miles
Highway driving maximum distance: 32 mpg × 15 gallons = 480 miles

So the compound inequality is:

360 miles ≤ distance ≤ 480 miles