Quadratic Word Problems with Consecutive Integers

The sum of three consecutive integers is 72. What are the integers?

• 23, 24, 25

• 20, 21, 22

• 21, 22, 23

• 25, 26, 27

If the first of three consecutive integers is represented as x, write a quadratic equation to express the product of these integers. What is the equation?

• x^3 + 2x^2 + x = 0

• x^3 + 3x^2 + 2x = 0

• x^2 + 2x + 1 = 0

• x^3 + 4x^2 + 3x = 0

A rectangle's length is three times its width. If the width is represented as x, express the area as a quadratic function. What is the area when the width is 4?

• 64

• 12

• 48

• 36

The product of two consecutive integers is 56. What are the integers?

• 5 and 6

• 7 and 8

• 8 and 9

• 6 and 7

A number is 5 less than twice a consecutive integer. If the integer is x, write a quadratic equation and solve for x when the number is 3.

• 6

• 2

• 1

• 4

The sum of two consecutive integers is equal to the square of the first integer. Write the equation and find the integers.

• 2 and 3

• 1 and 2

• 0 and 1

• 3 and 4

If the first of three consecutive integers is x, express the sum of their squares as a quadratic equation. What is the sum when x is 5?

• 90

• 110

• 120

• 100

A basketball player scores points in three consecutive games: x, x+1, and x+2. If the total score is 54, find the scores for each game.

• 14, 15, 16

• 17, 18, 19

• 18, 19, 20

• 15, 16, 17

The difference between the square of a consecutive integer and the integer itself is 12. Write the quadratic equation and solve for the integer.

• 5

• 3 or -4

• 2

• -3

If the first of four consecutive integers is x, express the total of their cubes as a quadratic equation. What is the total when x is 2?

• 512

• 128

• 64

• 224