SOLUTION: 1. 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 whic

Question 119974: 1. 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 tp 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.
***Thanks from a frustrated dad trying to help his daughter.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1. An architect is designing a house for the Frazier 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 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.
:
There is 20 ft space on each side, so we can say
W =< 90 - 40
W =< 50 ft is the width of the house.
:
:
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.
:
For min of 2800 sq ft
50*L => 2800
L =>
L => 56 ft length for min area (56*50 = 2800)
:
For max of 3200
50L =< 3200
L =<
L =< 64 ft length for max area (64*50 = 3200)
:
You can say that any length at or between 56 and 64 will satisfy this requirement
:
:
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.
:
I'm not sure what they want here. I would just say:
Cost = 175000 +/- 20000:
:
Perhaps we can write an absolute equation like this:
Let = x actual cost of house
:
|x - 175000| =< 20000
;
solve if overbudget; let x = 190000
|190000 - 175000| =< 20000
15000 =< 20000; true
:
Solve if underbudget: let x = 163000
|163000 - 175000| =< 20000
|-12000| =< 20000
12000 =< 20000; true also
|
Not always sure what the latest is on these kind of problems. Hope this helps
RELATED QUESTIONS
hello if u can please help that would be great An architect is designing a house for... (answered by stanbon)

An architect is designing a house for the Frazier family. In the design he must consider... (answered by vleith)

I am unable to understand this question and I have tried doing it several times and I am... (answered by Theo)

An architect is designing a house for the mullet family. In the design he must consider... (answered by Theo)

An architect is designing a rectangular family room with a perimeter of 48\m. What... (answered by ikleyn)

an architect is allowed no more then 15 square meters to add a small bedroom to a house.... (answered by ankor@dixie-net.com)

An architect is considering bidding for the design of a gnu museum. The cost of drawling... (answered by ikleyn)

In Mississippi, a child is eligible for the Children�s Health Insurance Program (CHIP) if (answered by nerdybill)