Quadratic Adventures: Solving Consecutive Integer Puzzles

1. The product of two consecutive integers is 72. What are the integers?

• 8 and 9

• 7 and 8

• 6 and 7

• 9 and 10

2. If the product of three consecutive integers is 210, what are the integers?

• 3, 4, 5

• 5, 6, 7

• 6, 7, 8

• 4, 5, 6

3. A rectangle's length is one more than its width. If the area of the rectangle is 72 square units, what are the dimensions?

• Width: 9 units, Length: 10 units

• Width: 8 units, Length: 9 units

• Width: 5 units, Length: 6 units

• Width: 6 units, Length: 7 units

4. The product of two consecutive integers is equal to the square of the smaller integer. What are the integers?

• 1 and 2

• 2 and 3

• 0 and 1

• -1 and 0

5. A farmer has a rectangular field where the length is 3 meters longer than the width. If the area is 40 square meters, what are the dimensions of the field?

• Width: 6 meters, Length: 9 meters

• Width: 5 meters, Length: 8 meters

• Width: 4 meters, Length: 7 meters

• Width: 5 meters, Length: 10 meters

6. The product of two consecutive integers is 56. Can you find the integers and verify their roots?

• 8 and 9

• The integers are 7 and 8.

• 6 and 7

• 5 and 6

7. If the product of two consecutive integers is 90, what are the integers? Use the quadratic formula to find the roots.

• 7 and 8

• 10 and 11

• 8 and 9

• 9 and 10

8. A number and its consecutive integer have a product of 20. What are the two integers?

• 4 and 5

• 3 and 4

• 2 and 3

• 5 and 6

9. The area of a square is equal to the product of two consecutive integers. If the area is 36 square units, what are the integers?

• 5 and 6

• 6 and 7

• 4 and 5

• 3 and 4

10. If the product of two consecutive integers is 42, what are the integers? Model this problem with a quadratic equation and find the roots.

• 4 and 5

• 5 and 6

• 7 and 8

• 6 and 7