Quadratic Word Problems

If you square 5 more than a positive number, the result is 88 more than 12 times the number. Find the positive number.

• -9

• 7

• 9

• -7

The Area of a rectange is 216 inches squared. The length of the rectangle can be represented by 2x +10 and its width can be represented by 3x. What are the dimensions of this rectangle in inches?

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A parking lot is to be enclosed by fencing and the available amount of fencing is 900 ft. what is the maximum amount of area that can be enclosed?

• 56250 sq. ft.

• 52650 sq. ft.

• 50625 sq. ft.

• 55620 sq. ft.

If you square 5 more than a positive number, the result is 88 more than 12 times the number.  Find the numbers.

• -9, 7

• √75

• 9, -7

• 15, -5

The sum of a number and its square is 72. Find the number(s).

• 8 or 9

• 8 or -9

• -8 or 9

• -8 or -9

Suppose that the equation V = 20.8x² – 458.3x + 3,500 represents the value of a car from 1964 to 2002. What year did the car have the least value? (x = 0 in 1964) 

• 1965

• 1970

• 1975

• 1980

The sum of a number and its square is 72. Find the number.

• 8 or 9

• 8 or -9

• -8 or 9

• -8 or -9

If you square 5 more than a positive number, the result is 88 more than 12 times the number. Find the number.

• 7

• -7

• 9

• -9

One number is 3 more than another. The sum of their squares is 149. Find the numbers.

• 4 and 7; -4 and -7

• 5 and 8; -5 and -8

• 6 and 9; -6 and -9

• 7 and 10, -7 and -10

The original plan for Mr. Harris’s house is a rectangle that measures 40’ x 50’. Because of an increase in cost, the square footage of the house must be decreased to 1739 square feet. To do this, the length and width will be decreased by the same amount. By how much should they be decreased?

• 6 ft

• 43.5 ft

• 3 ft

• 1.5 ft