Quadratic Equations - Word Problems

1. Quadratic Equations - Word Problems 4.7B.9 MATHPOWERTM 11, WESTERN EDITION

2. 1. The side of one square is 3 cm longer than the side of another. If their combined area is 117 cm2, find the dimensions of each square. Let x = side of the smaller square. Let x+3= side of the larger square. Therefore, the smaller square is 6 cm x 6 cm. x2 + (x + 3)2 = 117 x2 + x2 + 6x + 9 =117 2x2 + 6x + 9 = 117 2x2 + 6x - 108 = 0 2(x2 + 3x - 54) = 0 2(x + 9)( x - 6) = 0 x = -9 or x = 6 The larger square is 9 cm x 9 cm. Not possible 4.7B.11

3. 2. A factory is to be built on a lot that measures 80 m by 60 m. A lawn of uniform width and equal in area to the factory, must surround the factory. How wide is the strip of lawn, and what are the dimensions of the factory? Let x =the width of the strip. x Area of the factory: x x 60 60 - 2x 2400 = (80 - 2x)(60 - 2x) 2400 = 4800 - 280x + 4x2 0 = 4x2 - 280x + 2400 0 = 4(x2 - 70x + 600) 0 = 4(x - 60)(x - 10) x = 60 or x = 10 80 - 2x x 80 Total area = 80 x 60 = 4800 m2 Area of the factory: Therefore, the strip is 10 m wide, and the factory is 60 m x 40 m. = 2400 m2 4.7B.12

4. At a concert for Keshia at Rexall Place the entire stadium will sell • out if the ticket prices are $35. Rexall can hold 17500 people. The • Concert organizers know that if they will lose 300 patrons for • every $5 increase in price. • Define the variable for this situation • Write an expression for the ticket price using your variable • Write an expression for the number of patrons that will attend • What ticket price should the organizers have to make at least • $1 000 000 in total receipts 4.7B.13