Answer:
$53
Step-by-step explanation:
Given that, two type of clothes nylon and wool carpet.
Let the price of one yard of nylon carpet = $[tex]x[/tex]
Let the price of one yard of wool carpet = $[tex]y[/tex]
Price for 16 yd of nylon carpet and 22 yd of wool carpet = $1902
Price for 20 yd of nylon carpet and 21 yd of wool carpet = $2033
Writing equations as per given statement:
[tex]16x+22y=1902 ...... (1)\\20x+21y=2033 ...... (2)[/tex]
Here, we have to find the value of [tex]y[/tex].
By equation (1), we get:
[tex]16x = 1902 - 22y \\\Rightarrow x = \dfrac{1}{16}(1902-22y) ..... (3)[/tex]
Putting the value from equation (3) to equation (2):
[tex]20 (\dfrac{1}{16}(1902-22y) ) + 21y =2033\\\Rightarrow 9510-110y + 84y = 8132\\\Rightarrow 26y=1378\\\Rightarrow \bold{y = 53}[/tex]
Therefore, the cost per yard for the wool carpet is $53.
