Solving Equations by Factoring
Directions: Write and solve a quadratic equation for each story problem below.
1) The product of 12 times Karl’s age reduced by 72 and twice his age is zero. How old is
Karl?
2) Mr. Steinmetz had a square garden. He was able to triple the area of the garden by
increasing the length by 18 feet. What were the original dimensions of his garden?
3) The length of a rectangular playground is ten yards less than three times the width. In order
to add a baseball diamond next to it, the width of the playground is decreased by 15 yards and
the length is decreased by 35 yards. The area of this reduced playground is 675 square yards.
What are the original dimensions of the playground?
4) The product of 2 consecutive integers is 110. What are the integers?
5) The sum of two integers is 15 and their product is 44. What are the integers?
6) Patty has a photograph that is 8 cm by 6 cm. She needs to reduce length and width by the
same amount. The area of the new picture will be exactly ½ of the original picture. By what
amount should the length and width be reduced?
7) A rectangle is 4” by 7”. When the length and width are increased by the same amount, the
area is increased by 26 square inches. By what amount was the rectangle increased?
8) Find two consecutive even integers whose product is 624.
9) When the square of the second of two consecutive even integers is added to twice the first
integer, the sum is 76. What are the integers?
KEY
1) Karl is 6 years old
2) 9 ft by 9 ft
3) 30 yards by 80 yards
4) the numbers are 10 and 11 or – 10 and – 11
5) 4 AND 11
6) 2 cms each
7) 2 inches each
8) 24 and 26 or – 24 and – 26
9) 6,8 or – 12. – 10
Solving Equations by Factoring
Directions: Write and solve a quadratic equation for each story problem below.
1) The product of 12 times Karl’s age reduced by 72 and twice his age is zero. How old is
Karl?
2) Mr. Steinmetz had a square garden. He was able to triple the area of the garden by
increasing the length by 18 feet. What were the original dimensions of his garden?
3) The length of a rectangular playground is ten yards less than three times the width. In order
to add a baseball diamond next to it, the width of the playground is decreased by 15 yards and
the length is decreased by 35 yards. The area of this reduced playground is 675 square yards.
What are the original dimensions of the playground?
4) The product of 2 consecutive integers is 110. What are the integers?
5) The sum of two integers is 15 and their product is 44. What are the integers?
6) Patty has a photograph that is 8 cm by 6 cm. She needs to reduce length and width by the
same amount. The area of the new picture will be exactly ½ of the original picture. By what
amount should the length and width be reduced?
7) A rectangle is 4” by 7”. When the length and width are increased by the same amount, the
area is increased by 26 square inches. By what amount was the rectangle increased?
8) Find two consecutive even integers whose product is 624.
9) When the square of the second of two consecutive even integers is added to twice the first
integer, the sum is 76. What are the integers?
KEY
1) Karl is 6 years old
2) 9 ft by 9 ft
3) 30 yards by 80 yards
4) the numbers are 10 and 11 or – 10 and – 11
5) 4 AND 11
6) 2 cms each
7) 2 inches each
8) 24 and 26 or – 24 and – 26
9) 6,8 or – 12. – 10