Solving Word Problems Involving Quadratic Equations

Translate: The square of a number is one hundred fifty more than five times a number.

• x² = 5x + 150

• x² = 5x + 50

• 2x = 5x + 150

• x² = 5x + 15

Translate " four less than the square of a number is negative eight" into mathematical equation.

• x² - 4 = -8

• x² + 4 = -8

• 2x - 4 = -8

• 2x + 4 = -8

Ate Marwin and Ate Daisy are both working on the school canteen. Together they can finish cleaning the canteen in 4 hours. It takes ate Marwin working alone in 6 hours longer than it takes Ate Daisy working alone. Determine the quadratic equation formed on the given problem.

• x² + 6x + 12 = 0

• x² + 2x + 24 = 0

• x² - 6x + 12 = 0

• x² – 2x – 24 = 0

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

The sum of the square of two consecutive positive integers is 85. Write a quadratic equation.

• x² + x - 1 = 85

• x² + x + 1 = 85

• x² + x - 42 = 0

• x² + x + 42 = 0

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 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

The height of an item falling can be modeled by h_t = -16t² + h_o . Where h_o is the initial height in feet, and h_t is the height in feet at time t in seconds. If I drop a penny at a height of 18.6 feet, how long will it take the item to hit the ground?

• 1.08 seconds

• 2.08 seconds

• 0.08 seconds

• 1.17 seconds

The number of bags of peanuts sold at the Kennedy Center from 1900 to 2004 can be modeled by S = 4t² + t - 3, where t is the number of years since 1900. How many bags of peanuts were sold in 2000?

• 40,050

• 40,097

• 19,997

• 98