Question

a contractor buys 20 yds of nylon carpet and 30 yds of wool carpet for $860. A second purchase, at the same prices, includes 24 yds of nylon carpet and 32 yds of wool carpet for $984. Find the cost per yard of the wool carpet.

Answer 1

The cost per yard of wool carpet can be determined by solving a system of linear equations obtained from the given purchases. Through the elimination method, the system reveals that the cost per yard of wool carpet is $24.5.

Step-by-step explanation:

To find the cost per yard of wool carpet, we can set up a system of linear equations based on the given purchases. Let x be the cost per yard of nylon carpet and y be the cost per yard of wool carpet.

From the first purchase, we have the equation:

20x + 30y = 860

From the second purchase, we have the equation:

24x + 32y = 984

We can solve this system of equations using substitution or elimination. In this case, let's use elimination.

First, we multiply the first equation by 8 and the second by 5 to align the coefficients of x:

160x + 240y = 6880 (Equation 1 multiplied by 8)

120x + 160y = 4920 (Equation 2 multiplied by 5)

Next, we subtract the second equation from the first to eliminate x:

40x + 80y = 1960

Diving both sides of the equation by 80 gives us:
y = 24.5

Therefore, the cost per yard of wool carpet is $24.5.