Download Quadratic Relationships Word Problems

Quadratic Relationships Word Problems
Finding Unknown Numbers
1. Find three consecutive odd integers such that the square of the first increased the product of the other two is
224.
2. The product of two consecutive odd integers is 99. Find the integers.
3. Find two consecutive positive integers such that the square of the first is decreased by 17 equals 4 times the
second.
4. When the square of a certain number is diminished by 9 times the number the result is 36. Find the number.
5. A certain number added to its square is 30. Find the number.
6. The square of a number exceeds the number by 72. Find the number.
7. Find two positive numbers whose ratio is 2:3 and whose product is 600.
Geometry
1. The altitude of a triangle is 5 less than its base. The area of the triangle is 42 square inches. Find its base and
altitude.
2. The length of a rectangle exceeds its width by 4 inches. Find the dimensions of the rectangle it its area is 96
square inches.
3. If the measure of one side of a square is increased by 2 centimeters and the measure of the adjacent side is
decreased by 2 centimeters, the area of the resulting rectangle is 32 square centimeters. Find the measure of
one side of the square.
4. Joe’s rectangular garden is 6 meters long and 4 meters wide. He wishes to double the area of his garden by
increasing its length and width by the same amount. Find the number of meters by which each dimension must
be increased.
Revenue/Profit (Revenue = # of sales x price)
1. The current price of an amateur theater tickets is $20, and the venue typically sells 500 tickets. A
survey found that for each $1 increase in ticket price, 10 fewer tickets are sold.
a) What is the number of $1 increases in price that will maximize the revenue?
b) What price per ticket will maximize the revenue?
c) What is the maximum revenue?
2. A sticker warehouse sells an average of 6 rolls of stickers per customer at $4 per roll. Statistics show
that for every $0.25 decrease in price, customers will buy an additional roll.
a) According to this model, if the stickers were reduced to $3 per roll, what will be the revenue?
b) According to this model, at which sticker price will the revenue from stickers be $28?
3. A manufacturer has been selling light bulbs for $2.00 each. People have been buying 100 light bulbs
per month. The manufacturer believes that for every $1.00 increase per bulb, 4 fewer bulbs will be sold
each month. It costs the manufacturer $.50 to make each light bulb. Assume the manufacturer sells
every light bulb that he makes and that any whole number of light bulbs can be made.
a) What price should the manufacturer sell each light bulb to make the maximum profit each month?
b) How many light bulbs will maximize the manufacturer's monthly profit?
c) What is the manufacturer's monthly profit?