Assignment #47: Quadratic Story Problems II
Example:
Bface had a 3 ft. by 5 ft. rectangular sandbox. He decided to add a bench around it, of uniform
width. When he finished, he noticed that the area of the bench was one-third of the area of
the sandbox. How wide was the bench?
Solution: Let the width be x. The dimensions of the sandbox and bench together are now 3+2x
and 5+2x.
From the story, we know the sandbox has an area of 15 (3 times 5) and the bench has an area
that is one-third of the sandbox, or 1/3 times 15, which equals 5. Thus, the total area of the
sandbox and bench would be 20.
(3 + 2x)(5 + 2x) = 20
and now you can solve the quadratic equation
Problems for Assignment #47
1. The Chicago zoo sells a rare breed of rectangular squirrel, suitable for framing. The squirrel
measures 4 ft. by 5 ft. A recent customer, Kwunk, frames his squirrel with a frame of
uniform width. (The frame is shaded pink in the diagram below.) Kwunk discovers that the
frame plus the squirrel has an area of 110 square feet. Find the width of the frame.
2. Find the discriminant and write what it tells you about the solution(s). Do not solve.
4x2 – 9 = 0 (Hint: this is the same as 4x2 + 0x + –9 = 0 )
Find all the numbers that fit the given descriptions. Solve with quadratic equations.
3. The sum of the squares of two consecutive even integers is 52.
4. Find three consecutive odd integers such that the sum of the squares of the first two
integers is 7 less than the square of the last one.
(Optional): Find the units digit Y so that 9183Y is divisible by 11.