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.

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

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

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

thank you so much for your help

yw

May I bother you with another problem?

name it

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.

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

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

shorter one is 5, longer one is 16

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 \[3x+1=21-x\]

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.

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

but your makes more sense, thanks again

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