SOLUTION: How can I show the equation use for the solution? A coffee merchant has coffee beans that sell for $9 per pound and $12 per pound. The two types are to be mixed to create 100 lb

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Question 91968: How can I show the equation use for the solution?
A coffee merchant has coffee beans that sell for $9 per
pound and $12 per pound. The two types are to be mixed to create 100 lb of a mixture that will sell for $11.25 per pound. How much of each type of bean should be used in the mixture?
Answer by mathispowerful(115) About Me  (Show Source):
You can put this solution on YOUR website!

The idea is that the total worth of coffee will remain unchanged before and after mixture.
Let x represent the amount of $9-coffee
y represent the amount of $12-coffee
then
x + y = 100
9x + 12y = 11.25 * 100 = 1125
so we have
x + y = 100
9x + 12y = 1125
multiply -9 on both sides of first equation
-9x - 9y = -900
add to second equation
3y = 225
y = 75 lbs
and x = 100 -75 = 25 lbs
so we need to mix 25 lbs of $9-coffee with 75 lbs of $12-coffee.