Question 30901: heres another word problem: a clothing manufacturer purchased 100 yds of cotton and 50 yds of wool for a total cost of $125. Another purchase, at the same prices, included 70 yds of cotton and 40 yds of wool for a total cost of $90.Find the cost per yard of the cotton and wool.
Answer by blubunny01(20)   (Show Source):
You can put this solution on YOUR website! 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.
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