A contractor buys 14 yd of nylon carpet and 20 yd of wool carpet for $1738. A second purchase, at the same prices, includes 16 yd of nylon carpet and 25 yd of wool carpet for $2102. Find the cost per yard of the wool carpet.
If they cost $n and $w per yard, then we have
14n+20w = 1738
16n+25w = 2102
Now just solve for n and w.
To find the cost per yard of the wool carpet, we need to set up a system of equations and solve it.
Let's represent the cost per yard of the nylon carpet as "x" dollars, and the cost per yard of the wool carpet as "y" dollars.
From the given information, we can set up the following equations:
Equation 1: 14x + 20y = 1738
Equation 2: 16x + 25y = 2102
We now have a system of linear equations that we can solve.
One way to solve this system is by the substitution method. We will solve Equation 1 for x and substitute it into Equation 2.
From Equation 1, we get:
14x = 1738 - 20y
Simplifying further, we have:
x = (1738 - 20y)/14
Substituting this value of x into Equation 2, we have:
16((1738 - 20y)/14) + 25y = 2102
To simplify this equation, we can multiply both sides by 14 to get rid of the fraction:
16(1738 - 20y) + 350y = 29428
Expanding and combining like terms:
27728 - 320y + 350y = 29428
Simplifying further:
30y = 1700
Finally, solving for y, we divide both sides by 30:
y = 1700/30
y = 56.67
Therefore, the cost per yard of the wool carpet is approximately $56.67.