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

Bethani Gasparine

A shipping company is loading boxes onto a truck. The truck can carry a maximum of 6 500 pounds of cargo. If each box weighs 100 pounds, write and solve an inequality that can be used to find the number of boxes loaded onto the truck.

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Video Transcript

A shipping company is loading boxes onto a truck. The truck can carry a maximum of six thousand five hundred pounds of cargo. If each box weighs one hundred pounds, write and solve an inequality that can be used to find the number of boxes loaded onto the truck.

First, let’s begin by letting π‘₯ represent the number of boxes that were loaded onto the truck. So we have π‘₯, the number of boxes, and each box weighs one hundred pounds. So however many boxes there are, we need to multiply that by one hundred.

Then it says that the truck can carry a maximum of six thousand five hundred pounds. So that means if the maximum weight is six thousand five hundred, then we can’t load more than that amount. So it has to be either less than that amount or exactly equal to that amount. So we have one hundred π‘₯ is less than or equal to six thousand five hundred.

Now in order to solve our inequality, so to solve for π‘₯, we divide both sides by one hundred. And when we do that, π‘₯ is less than or equal to sixty-five because six thousand five hundred divided by one hundred, divided by one hundred, is equal to sixty-five. This means sixty-five boxes, or less than sixty-five boxes can be loaded onto this truck.

So again, our inequality would be one hundred π‘₯ is less than or equal to six thousand five hundred. And after solving our inequality, we find that π‘₯ is less than or equal to sixty-five.