SOLUTION: Cynthia Besch wants to buy a rug for a room that is 23 ft wide and 24 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 240 square feet of

Algebra.Com
Question 1084975: Cynthia Besch wants to buy a rug for a room that is 23 ft wide and 24 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 240 square feet of carpeting. What dimensions should the rug​ have?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
x, the uniform strip size along each side.
Rug dimensions, 23-2x and 24-2x.
Rug AREA given, 240 square feet.


Simplify and solve this equation for x, and then evaluate the rug's dimensions.
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Your working equation to find the unknown width x of the uniform strip is 

(23-2x)*(24-2x) = 240.


So, the question is: find two factors of the number 240 that differ in one unit.


You can find the solution MENTALLY: these factors are 15 and 16.


So, 23-2x = 15, which implies 2x = 23 - 15 = 8 and x = 4 feet.


Thus the width of the uniform strip is 4 feet.


It imlies that the dimensions of the rug are 24 - 2*4 = 16 feet (length) and 23 - 2*4 = 15 feet (width).

Solved (mentally).

You can get the same answer using other methods.
RELATED QUESTIONS

Cynthia Besch wants to buy a rug for a room that is 23 ft wide and 30 ft long. She wants... (answered by josmiceli,Theo)
Cynthia Besch wants to buy a rug for a room that is 17 ft wide and 24 ft long. She wants... (answered by Theo)
Cynthia Besch wants to buy a rug for a room that is 24 ft wide and 25 ft long. She wants... (answered by ikleyn)
Cynthia Besch wants to buy a rug for a room that is 23 ft wide and 32 ft long. She wants... (answered by josgarithmetic)
Cynthia Besch wants to buy a rug for a room that is 18 ft wide and 31 ft long. She wants... (answered by josmiceli)
Cynthia Besch wants to buy a rug for a room that is 18 ft wide and 31 ft long. She wants... (answered by ikleyn,jorel1380)
Cynthia Besch wants to buy a rug for a room that is 24 ft wide and 30 ft long. She wants... (answered by josgarithmetic)
cynthia besch wants to buy a rug for a room that is 12 ft wide and 15 ft long. she wants... (answered by mananth)
Cynthia Besch wants to buy a rug for a room that is 11 ft. wide and 30 ft. long. She... (answered by ankor@dixie-net.com)