Video: Writing and Solving One-Step Linear Inequality Word Problems

Elizabeth wants to buy some goldfish. She can only spend up to $27, and the fish cost $3 each. Write an inequality to find how many goldfish Elizabeth can buy, and then solve it.

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Video Transcript

Elizabeth wants to buy some goldfish. She can only spend up to 27 dollars, and the fish cost three dollars each. Write an inequality to find how many goldfish Elizabeth can buy, and then solve it.

Well, to solve this problem. First of all, we’ll look at the key information. The first bit of information we have is that she can only spend up to 27 dollars. So we say that the total spend then is less than or equal to 27 dollars. We also know that the cost of fish is three dollars. And we’re gonna say that the number of fish is equal to 𝑥. You could use any letter here but we’re using 𝑥 as our number of fish.

Okay. Now we can use this to write our inequality. So if we know that Elizabeth is gonna buy fish, we could say that actually the total cost of the fish that she’s going to buy is gonna be equal to three, because that’s the price of one fish, multiplied by 𝑥, and that’s because that’s our number of fish. Okay, great. So this is an expression for the total cost of fish. Now we can complete our inequality because we know that our total spend needs to be less than or equal to 27, 27 dollars but we’re just gonna write as 27 in our inequality.

So great, we’ve now got our inequality. All we need to do now is solve it. And to do that, we just treat it like we treat any equation. So we’re going to divide both sides by three which gives us an answer of 𝑥 is less than or equal to nine. So therefore, we can say that the number of fish Elizabeth can buy can be represented by: 𝑥 is less than or equal to nine.

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