1. An architect is designing a house for the Mullet family. In the design he must consider the desires of the family and the local building codes. The rectangular lot on which the house will be built has 91 feet of front age on a lake and is 158 feet deep. a. The building codes state that one can build no closer than 10 feet to the lot line. Write an inequality and solve to see how long the front of the house facing the lake may be.

b. The Mullets requested that the house contain no less than 2800ft2 and no more than 3200 ft2 of floor space. Write an inequality to represent the range of permissible widths for the house.

c. The Mullets 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. Give the meaning of the answer.

a) x ≤ 71

b) 2800/L ≤ w ≤ 3200/L

c) x ≤ 195,000 and x ≥ $155,000

Step-by-step explanation:

An architect is designing a house for the Mullet family.

The rectangular lot on which the house will be built has 91 feet of frontage on a lake and is 158 feet deep. The building codes state that one can build no closer than 10 feet to the lot line.

a) Write an inequality and solve to see how long the front of the house facing the lake may be.

Let x represents the width of the house facing the lake.

Since we cannot build closer than 10 feet to the lot line on each side of the house and the width is 91 feet then

x + 2(10) ≤ 91

x + 20 ≤ 91

x + 20 - 20 ≤ 91 - 20

x ≤ 71

So that means the width of the house facing the lake should be less than or equal to 71 feet.

b. The Mullets requested that the house contain no less than 2800 ft² and no more than 3200 ft² of floor space. Write an inequality to represent the range of permissible widths for the house.

We are given that the area of house should contain no less than 2800 ft² and no more than 3200 ft² of floor space,

Mathematically,

2800 ≤ A ≤ 3200

Since Area = width*length

2800 ≤ w*L ≤ 3200

2800/L ≤ w ≤ 3200/L

This is the required inequality that would give us the permissible widths for the house, where the length L can have any value less than or equal to 71 feet.

For example, if the length is 71 feet then

2800/L ≤ w ≤ 3200/L

2800/71 ≤ w ≤ 3200/71

39.44 ≤ w ≤ 45.07

c) The Mullets 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. Give the meaning of the answer.

So the cost of the house is $175,000 and the deviation is $20,000.

Mathematically,

± (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

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