Math 20-1 Quadratic Equations Word Problems - Notes
1. A picture that measures 30 cm by 20 cm is to be surrounded by a frame of uniform width and equal in
area to the picture. How wide is the frame, and what are the dimensions of the entire framed picture?
2. The length of a rectangle is 2 less than three times the width. Find the dimensions of the rectangle if
the area is 65 square meters.
3. Find two consecutive even integers such that the square of the smaller is 10 more than the larger.
4. A ladder is resting against a wall. The top of the ladder touches the wall at a height of 15 feet. Find the
distance from the wall to the bottom of the ladder if the length of the ladder is one foot more than twice
its distance from the wall.
5. Write a quadratic equation with the following roots
a. 6 and 7
b. 2/3 and -1/2.
Is it possible to write another quadratic equation with the same roots? Explain.
6. You have a 500-foot roll of fencing and a large field. You want to construct a rectangular playground
area. What are the dimensions of the largest such yard? What is the largest area?
Practice
1. The product of two consecutive odd integers is 99. Find the integers.
2. The longer leg of a right triangle is ten less than three times the shorter leg. The hypotenuse is 4 more
than the shorter leg. Find the length of the shorter leg.
3. You run a canoe-rental business on a small river in Ohio. You currently charge $12 per canoe and
average 36 rentals a day. An industry journal says that, for every fifty-cent increase in rental price, the
average business can expect to lose two rentals a day. Use this information to attempt to maximize
your income. What should you charge?
4. Two cars leave an intersection. One car travels north; the other travels east. When the car traveling
north had gone 24 miles, the distance between the cars was four miles more than three times the
distance traveled by the car heading east. Find the distance between the cars at that time.
5. The width of a rectangle is 11 inches less than its length. Find the dimensions of the rectangle if the
area is 80 square inches.
6. Find three consecutive integers such that four times the sum of all three is 2 times the product of the
larger two.
Solutions: 1) 9,11 or -9, -11
2) 6
3) $10.50
4) 25 miles
5) w = 5 l = 16
6) 4, 5, 6 or -1, 0, 1