Video: Finding the Difference between Two Integers with Different Signs in Word Problems

During a yard sale, Anthony had two pairs of shoes that he expected to sell for the same price. One pair of shoes sold for $5 more than expected and the other sold for $2 less than expected. What was the difference between the selling prices?

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Video Transcript

During a yard sale, Anthony had two pairs of shoes that he expected to sell for the same price. One pair of shoes sold for five dollars more than expected and the other sold for two dollars less than expected. What was the difference between the selling prices?

We have shoe number one and shoe number two. Anthony expected them both to be sold for the same price. We’ll call that 𝑃. Shoe number one sold five more than expected, 𝑃 plus five. Shoe number two sold two less than expected, 𝑃 minus two.

We find the difference between the selling prices by taking the price of shoe one 𝑃 plus five and subtracting the price of shoe two 𝑃 minus two. 𝑃 plus five and then we distribute our subtraction minus 𝑃 minus a negative would be plus two. Combine like terms. Positive 𝑃 minus 𝑃 cancels out and five plus two equals seven.

The price difference between the two pairs was seven dollars.

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