Honors GeometryName ANSWERS .
Solving Quadratic Word ProblemsPeriod_____Date______
DIRECTIONS: Onyourownpaper, set up equations and solve each of the following problems.
1.) If you subtract a number from four times its square, the result is three. Find that number.
4x2 – x = 3The number could be 1 or -3/4.
2.) Eight more than the square of a number is six times that number. Find the number.
8 + x2 = 6xThe number could be 4 or 2.
3.) The product of two consecutive integers is 182. Find these two integers.
(Hint: If x represents an integer, how could you represent the next consecutive integer –- what would you count by?)
Consecutive integers could be represented as x and (x + 1).
x(x + 1) = 182The integers are 13,14 or -14,-13.
4.) The product of two consecutive even integers is 168. Find these two integers.
(Hint: For even integers, what would you would count by?)
Consecutive evenintegers could be represented as x and (x + 2).
x(x + 2) = 168The numbers are 12,14 or -14,-12.
5.) The product of two consecutive odd integers is 255. Find these two integers.
Consecutive oddintegers could be represented as x and (x + 2).
x(x + 2) = 255The numbers are 15,17 or -17,-15.
6.) The length of a rectangle is 4 m greater than its width. The area of this rectangle is
96 m2. Find the length and width.
If the width of the rectangle is w, then its length can be represented as (w+ 4).
w(4 + w) = 96The length is 12 mandthe width is 8 m.
7.) The measure of the area of a square is 5 feet more than its perimeter. Find the length
of aside.
x 2 = 5 + 4xThe side has length 5 feet.
8.) The base of a triangle is 10 cm larger than its height. The area of this triangle is
28 cm2. Find the height and base.
If the height of the triangle is h, then its base can be represented as (10 + h).
½h(10 + h) = 28The height is 4 cm and the base is 14 cm.
9.) If the sides of a square are lengthened by 3 m, the area becomes 81 m2. Find the length
of a side of the original square.
(x + 3) 2 = 81The original square had sides of length 6 cm.
10.) The sum of the squares of two consecutive odd positive integers is 74. Find these two
numbers.
Consecutive oddintegers could be represented as x and (x + 2).
x 2 + (x + 2)2 = 74The consecutive positive integers are 5,7.
11.) Mark threw a baseball upward with a speed of 19.6 meters per second. The physical
science formula h = rt – 4.9t2 gives the height of an object projected upward at a
rate of r meters per second after t seconds.
a) After how many seconds will the ball reach a height of 14.7 meters?
14.7 = 19.6t – 4.9t 2The ball is at that height after 1 or 3 sec.
b) After how many seconds will the ball hit the ground?
0 = 19.6t – 4.9t2The ball hits the ground after 4 seconds.
12.) The total surface area of a box is 350 m2. The box is 9 m high and has a square base.
Find the length of the side of the base.
2x 2 + 4*9x = 350The side of the base has length 7 m.
13.) The cube of a number is the same as twice the square of the number. Find the number.
x3 = 2x2The number could be 2 or 0.
PSAT Challenge Problems:
14.) Find two consecutive positive numbers such that the product of the sum and difference of
the numbers plus eight is the sum of their squares.
Consecutive integers could be represented as x and (x + 1).
(x + (x + 1))*(x – (x + 1)) + 8 = x2 + (x + 1) 2
The positive numberswould be 2,3.
15.) An open rectangular gutter is made by turning up the
sides of a piece of metal 20 inches wide. The area of d 50 in2 d
the cross section of the gutter is 50 in2. Find the d 20 – 2d
depth of the gutter.
20 in
h(20 – 2h) = 50The depth of the gutter would be 5 inches.