Question 30901
This problem asks you to find two unknowns: cost/yard of cotton, and cost/yard of wool.


Let x = cost/yard of cotton.
Let y = cost/yard of wool.


We know that a clothing manufacturer purchased 100 yds of cotton and 50 yds of wool for a total cost of $125.  So, to put this into an equation, we have:
100x + 50y = 125.


We also know that a purchase was made for 70 yds of cotton and 40 yds of wool for a total cost of $90.  Again, to put this into an equation, we have:
70x + 40y = 90.


Now you have two equations for two unknowns, and there are several ways to solve these types of problems.  For simplicity, I'll use the substitution method.


I'll take 100x + 50y = 125 and solve for x:
100x = 125 - 50y
   x = (125/100) - (50/100)y
   x = (5/4) - (1/2)y


Then I'll substitute it into the second equation, 70x + 40y = 90.
70[(5/4) - (1/2)y] + 40y = 90.  


Now, I can solve for y.

70[(5/4) - (1/2)y] + 40y = 90.  

[87.5 - 35y] + 40y = 90

87.5 + 5y = 90

5y = 2.5
y = 0.5


Now, we can go back to the previous equation and solve for x:
x = (5/4) - (1/2)y
x = (5/4) - (1/2)(0.5)
x = (5/4) - (1/4)
x = 1


This means, the cost of cotton is $1.00, and the cost of wool is $0.50.