SOLUTION: Purchasing: a contractor buys 16yds of nylon carpet and 20 yds of wool carpet for $1840. A second purchase, at the same prices, includes 18 yds of nylon carpet and 25 ydss of wool
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Question 164614: Purchasing: a contractor buys 16yds of nylon carpet and 20 yds of wool carpet for $1840. A second purchase, at the same prices, includes 18 yds of nylon carpet and 25 ydss of wool carpet for $2200. Find the cost per yard of the wool carpet?
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Purchasing: a contractor buys 16yds of nylon carpet and 20 yds of wool carpet for $1840. A second purchase, at the same prices, includes 18 yds of nylon carpet and 25 ydss of wool carpet for $2200. Find the cost per yard of the wool carpet?
:
Let w = cost/yd for wool
Let n = cost/yd for nylon
:
Write an equation for each statement:
;
"contractor buys 16yds of nylon carpet and 20 yds of wool carpet for $1840."
16n + 20w = 1840
:
" 18 yds of nylon carpet and 25 yds of wool carpet for $2200"
18n + 25w = 2200
:
Find the cost per yard of the wool carpet?
:
The want the price of the wool, so let's eliminate n
Multiply the 2nd equation by 16, multiply the 1st equation by 18; results;
:
288n + 400w = 35200
288n + 360w = 33120
---------------------subtraction eliminates n, find w
40w = 2080
w =
w = $52 a yd for wool
:
:
In order to check our solution we need to find the price of nylon
Using the 1st equation, substitute 52 for w
16n + 20(52) = 1840
16n + 1040 = 1840
16n = 1840 - 1040
16n = 800
n =
n = $50 a yd for nylon
:
Check our solution in the 2nd equation:
18(50) + 25(52) = 2200
900 + 1300 = 2200; confirms our solution
:
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