If the product of two consecutive integers is 72, which of the following pairs could represent those integers?
Practice Questions
1 question
Q1
If the product of two consecutive integers is 72, which of the following pairs could represent those integers?
8 and 9
6 and 7
5 and 6
4 and 5
The product of 6 and 7 is 42, while 8 and 9 gives 72. Therefore, the correct pair is 8 and 9.
Questions & Step-by-step Solutions
1 item
Q
Q: If the product of two consecutive integers is 72, which of the following pairs could represent those integers?
Solution: The product of 6 and 7 is 42, while 8 and 9 gives 72. Therefore, the correct pair is 8 and 9.
Steps: 7
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.
