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Video: Writing and Solving Linear Inequalities in a Real-World Context

Bethani Gasparine

A rental car company charges $65 plus an additional $0.72 per mile to rent a car. If Martin does not want to spend more than $290 for his rental car, write and solve an inequality to find how many miles he can drive.

01:25

Video Transcript

A rental car company charges 65 dollars plus an additional 72 cents per mile to rent a car. If Martin does not wanna spend more than 290 dollars for his rental car, write and solve an inequality to find how many miles he can drive.

Letโ€™s first let ๐‘ฅ represent the number of miles that Martin could drive. So the rental car company charges a fixed 65 dollars plus 0.72, so 72 cents, per mile, so times ๐‘ฅ, the number of miles. And this needs to be less than or equal to 290 because Martin doesnโ€™t wanna spend more than 290.

So the first thing we need to do is subtract 65 from both sides of the inequality. So now we have 0.72๐‘ฅ is less than or equal to 225. So now we need to divide both sides by 0.72 resulting in ๐‘ฅ is less than or equal to 312.5.

So Martin can drive up to 312.5 miles. Normally, we write the variables first with an inequality or equation. So we have that 0.72๐‘ฅ plus 65 is less than or equal to 290 resulting in, when solved, ๐‘ฅ is less than or equal to 312.5.