Application problem

Question

A contractor buys 18 yd of nylon carpet and 18 yd of wool carpet for $1800. A second purchase, at the same prices, includes 16 yd of nylon carpet and 23 yd of wool carpet for $1964. Find the cost per yard of the wool carpet.

Answer 1

To solve this, first one must write out the system of equations. I'll use n to represent the number of (square) yards of nylon, and w respectively for wool. The equations are then:

18n + 18w = 1800

16n + 23w = 1964

I notice the first equation has numbers all divisible by 18, so I can rewrite it as:

n + w = 100

Now, elimination or substitution is much easier. I'll go forward with elimination. If i subtract 16 of the first row from the second, it looks like:

16n + 23w = 1964

-(16n + 16w = 1600)

7w = 364

w = 364/7

From here, it's simply a matter of plugging w back in to the first equation!