Exploring Quadratics: Consecutive Integer Challenges

The sum of three consecutive integers is 72. What are the integers? Use the quadratic formula to find your answer.

• 21, 22, 23

• 23, 24, 25

• 25, 26, 27

• 20, 21, 22

The product of two consecutive integers is 240. What are the integers? Factor the quadratic expression to solve.

• 15 and 16

• 14 and 15

• 12 and 13

• 16 and 17

A rectangle's length is three more than its width. If the area is 70 square units, find the dimensions using a quadratic equation.

• Width: 6 units, Length: 9 units

• Width: 7 units, Length: 10 units

• Width: 8 units, Length: 11 units

• Width: 5 units, Length: 8 units

The difference between the squares of two consecutive integers is 1. What are the integers? Use the quadratic formula to solve.

• -1 and 0

• 0 and 1

• 1 and 2

• 2 and 3

The sum of the squares of two consecutive integers is 85. What are the integers? Factor the quadratic expression to find your answer.

• 4 and 5

• 5 and 6

• 6 and 7

• 7 and 8

A number and its consecutive integer add up to 45. What are the integers? Use the quadratic formula to solve.

• 21 and 22

• 23 and 24

• 20 and 21

• 22 and 23

The product of three consecutive integers is 120. What are the integers? Factor the quadratic expression to find your answer.

• 3, 4, 5

• 5, 6, 7

• 4, 5, 6

• 2, 3, 4

The sum of four consecutive integers is 100. What are the integers? Use the quadratic formula to solve.

• 19, 20, 21, 22

• 21, 22, 23, 24

• 25, 26, 27, 28

• 23, 24, 25, 26

The area of a square is equal to the product of two consecutive integers. If the area is 56, what are the integers? Factor the quadratic expression.

• 5 and 6

• 6 and 7

• 7 and 8

• 8 and 9

The sum of the first n consecutive integers is 78. Find n using the quadratic formula.

• 20

• 12

• 10

• 15