Video: Using Variables to Represent Numbers and Write Inequalities When Solving a Real-World Problem

An online retailer offers free delivery when your purchase totals $50 or more. James is preparing his order. He has already chosen items which total $42. Write an inequality that describes the condition on 𝑝, the cost of the additional items he needs to order for him to benefit from free delivery.

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Video Transcript

An online retailer offers free delivery when your purchase totals 50 dollars or more. James is preparing his order. He has already chosen items which total 42 dollars. Write an inequality that describes the condition on 𝑝 the cost of the additional items he needs to order for him to benefit from free delivery.

So we need to write an inequality, which is like an equation except instead of an equal sign, we use less than, less than or equal to, greater than, or greater than or equal to. And we need to write it in terms of 𝑝 — the cost of the additional items. So let’s start from the beginning. In order to get free delivery, we have to spend 50 dollars or more — so greater than or equal to 50.

So James’s order needs to be greater than or equal to 50 dollars. So right now, he has 42 dollars’ worth of items in his cart. So he needs to add 𝑝, the additional items needed, to reach that 50-dollar goal. So if we would like our inequality to have 𝑝 by itself, that way we can describe 𝑝, we need to subtract 42 from both sides of the inequality. So on the left, the 42s cancel. And on the right, we have 50 minus 42. So this would be a way to describe the condition on 𝑝.

So 𝑝 needs to be greater than or equal to 50 minus 42. Simplifying that will also be another way to describe 𝑝. The condition on that 𝑝 would have to be greater than or equal to eight, meaning the additional items that he needs to order need to cost all together eight dollars or more.

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