Question

50. MODEL WITH MATHEMATICS An architect is designing a house for the Frazier family. In the design, she must consider the desires of the family and the local building codes. The rectangular lot on which the house will be built is 158 feet long and 90 feet wide.

a. The building codes state that one can build no closer than 20 feet to the lot line. Write an inequality to represent the possible widths of the house along the 90-foot dimension. Solve the inequality.


b. The Fraziers requested that the rectangular house contain no less than 2800 square feet and no more than 3200 square feet of floor space. If the house has only one floor, use the maximum value for the width of the house from part a, and explain how to use an inequality to find the possible lengths.



c. The Fraziers have asked that the cost of the house be about $175,000 and are willing to deviate from this price no more than $20,000. Write an open sentence involving an absolute value and solve. Explain the meaning of the answer

Answer 1

Explanation:

a. ± (x - $175,000) ≤ $20,000

When (x - $175,000) is positive then

(x - $175,000) ≤ $20,000

x ≤ $20,000 + $175,000

x ≤ 195,000

Which means that the maximum cost should not exceed $195,000.

When (x - $175,000) is negative then

-(x - $175,000) ≤ $20,000

x - $175,000 ≥ -$20,000

x ≥ -$20,000 + $175,000

x ≥ $155,000

Which means that the minimum cost should not be less than $155,000