Question

A carpet layer wisher to determine the cost of carpeting a rectangular room whose perimeter is 52 feet. Suppose that the lenght of the room is 4 feet more than its width. Find:
a. the length and width of the room;
b. the cost of the carpet if it costs $18.95 per square yard. Thanks.

Answer 1

a) solve
\[52 = 2x+2(x+4)\] for x

Answer 2

\[52=2x+2x+8\]
\[52=4x+8\]
\[44=4x\]
\[x=11\]
so dimensions are 11 by 15

Answer 3

and area is
\[11\times 15=165\]
finally
\[165\times \$18.95=\$3126.75\]

Answer 4

thank you so much for your help

Answer 5

yw

Answer 6

May I bother you with another problem?

Answer 7

name it

Answer 8

thanks

A carpenter needs 2 pieces of lumber which together are 21 feet long. The longer piece needs to be 1 foot longer than 3 times the length of the shorter piece. Find the lenght of each piece.

Answer 9

maybe we use two variables
\[x+y=21\]
\[x=3y+1\]

Answer 10

where x is the longer piece. so the first equation says
\[3y+1+y=21\]
\[4y+1=21\]
\[4y=20\]
\[y=5\]

Answer 11

shorter one is 5, longer one is 16

Answer 12

but please don't think there is any one right way to do this. you could have said
"let x = length of shorter one, then since the total is 21 to longer one must be 21 - x"
then solve
\[3x+1=21-x\]

Answer 13

or you could have solved for the longer one. it is really a matter of naming a variable and then coming up with two expressions that involve the variable.

Answer 14

see what i came up with was x+1f+3x=21f and came up with the same answer x=5

Answer 15

but your makes more sense, thanks again