If the product of two consecutive integers is 72, which of the following pairs c

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Question: If the product of two consecutive integers is 72, which of the following pairs could represent those integers?

Options:

Correct Answer: 6 and 7

Solution:

The product of 6 and 7 is 42, while 8 and 9 gives 72. Therefore, the correct pair is 8 and 9.

If the product of two consecutive integers is 72, which of the following pairs could represent those integers?

If the product of two consecutive integers is 72, which of the following pairs could represent those integers?

Step 1: Understand that consecutive integers are numbers that follow one after the other, like 6 and 7 or 8 and 9.
Step 2: Write down the equation for the product of two consecutive integers. If we let the first integer be 'n', then the next consecutive integer is 'n + 1'. The equation is n * (n + 1) = 72.
Step 3: Rearrange the equation to find n. This gives us n^2 + n - 72 = 0.
Step 4: Factor the quadratic equation. We need two numbers that multiply to -72 and add to 1. The numbers are 8 and -9.
Step 5: Set up the factors: (n - 8)(n + 9) = 0. This gives us n = 8 or n = -9.
Step 6: If n = 8, then the consecutive integers are 8 and 9. If n = -9, the consecutive integers are -9 and -8, but we are looking for positive integers.
Step 7: Check the product of 8 and 9: 8 * 9 = 72, which is correct.

Consecutive Integers – Understanding the definition and properties of consecutive integers, which are integers that follow each other in order.
Product of Integers – Calculating the product of two numbers and recognizing the relationship between their values.