College Algebra Word Problem

Question

Offspring will be playing at a concert venue that has a stage that is 4 yards X 5 yards. Stage crew has 10 square yards of room to create a border around the stage, to keep crowd attenders back. How wide should they make the border to use all 10 square yards of space? (The border must be the same width on all four sides.)

Answer 1

This is just like a garden an a walkway problem....or a picture and the frame problem.

 

The dimensions of the stage are 4 by 5. If the fence surrounds all sides of the stage and has a uniform width, you can represent the new rectangle  as 4+2x and 5+2x.

 

The new rectangle has an area of (4+2x)(5+2x) = 20 + 18x + 4x²

The old rectangle has an area of 20

 

The region that you're talking about is the difference of these 2 expressions which leads to the equation

4x² + 18x + 20 - 20 = 10

4x² + 18 x - 10 = 0

2x² + 9x - 5 = 0

(2x - 1)(x+5) = 0

x=1/2 or x=-5 (rejected since a length can't be negative)

 

So you must place the railing 1/2 of a yard away from the stage on all sides to result in the area being 10 sq yards.

 

Hope this helped