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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 6500 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.

02:08

Video Transcript

A shipping company is loading boxes onto a truck. The truck can carry a maximum of 6500 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.

So this truck can carry a maximum of 6500 pounds. So what does the word maximum mean? It means that that is the largest amount of weight that this truck can handle. So you cannot load any more weight than that, 6500. So we can actually put less than that into the trucking and it would be fine, but we can’t put more than that. So that would represent a less than sign. However, it says the maximum is 6500, which means it can actually handle that amount, just not more than that. So we can add an equal sign underneath that which you do so with just one line. So here’s what we have so far. We can have less than or equal to 6500 pounds.

So let’s introduce the boxes now. And we can let 𝑥 represent the number of boxes. To determine how many boxes can actually be loaded onto this truck, we have to take into account the weight of each box. And each box weighs 100 pounds, so for every box we have to multiply by 100. So this would be our inequality.

Now it also says to solve the inequality. So to solve for 𝑥, we need to divide both sides by 100. On the left, they cancel. And then a little trick in case we didn’t have a calculator. If you line up the decimal places, the zeros that are lined up directly next to the left of the decimal place, that are right next to each other, can cancel. So we have 65 divided by one which is 65. So this means the maximum number of boxes they can actually load is 65, or they could load less than that.

So since it said to write and solve, 100𝑥 less than or equal to 6500 would be how we wrote this inequality. And then solving the inequality, we got 𝑥 is less than or equal to 65.