Video: Form and Solve a Simple Inequality to Solve a Real Life Context Problem

A group is taking a packhorse on an expedition to carry their water. The packhorse can carry a maximum of 240 pounds. Given that the combined weight of the bags that the horse needs to carry is 22 pounds and each bottle of water weighs 4.4 pounds, what is the maximum number of water bottles that the horse can carry?

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Video Transcript

A group is taking a packhorse on an expedition to carry their water. The packhorse can carry a maximum of 240 pounds. Given that the combined weight of the bags that the horse needs to carry is 22 pounds and each bottle of water weighs 4.4 pounds, what is the maximum number of water bottles that the horse can carry?

We’re given a maximum weight that the horse can carry of 240 pounds. The weight maximum has to be greater than or equal to the weight of the bags plus the water bottles. Another way of saying that is the weight of the bags plus the weight of the water bottles cannot exceed the maximum weight the horse can carry. We know the bags weigh 22 pounds and that the weight of the water bottles will be equal to 4.4 times 𝑥, where 𝑥 is the number of water bottles the team brings.

To find out how many water bottles the team can bring, we first need to subtract the weight of the bags from the maximum weight the horse can carry. 240 minus 22 equals 218. And that means the leftover weight is 218 pounds for the water bottles. To find out exactly how many bottles that would be, we divide 218 by the 4.4 pounds each water bottle weighs. 218 divided by 4.4 equals 49.54 repeating. And so, we have a statement that says 49.54 repeating is greater than or equal to 𝑥. And that means 𝑥 must be less than or equal to 49.54 repeating. Since we can’t bring this 0.54 repeating part of a water bottle, we’ll round down to the nearest whole number of 49.

And we’ll say that the maximum water bottles the horse can carry is 49. It would definitely be worth plugging that 49 back into our original equation just to check. 4.4 times 49 is 215.6, plus 22 equals 237.6. And it is true that 240 is greater than 237.6. With 49 bottles, they would not exceed the weight limit. We can also see if we subtract 237.6 from 240, the weight limit, there’s only 2.4 pounds left before the group reaches the weight limit. This confirms that they could not take 50 water bottles. They can only take 49.