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. Ho

Question 63261This question is from textbook
: 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? This question is from textbook

Found 2 solutions by uma, jai_kos:
Answer by uma(370) (Show Source): You can put this solution on YOUR website!

Let x lb of the first type be mixed with y lb of the second type.
Then x + y = 100 --------------------(1)
Cost of x lb at $9 per lb = $ 9x
Cost of y lb at $ 12 per lb = $12y
Cost of 100 pb of the mixture = 100 * 11.25 = 1125
==> 9x + 12y = 1125 ------------------(2)
9x + 9y = 900 -----------------(1) x 9
Subtracting the above two equations we get...
3y = 225
==> 3y/3 = 225/3
==> y = 75
PLugging in y = 75 in (1) we get.. x = 25
Thus he has to mix 25 lb of $9 type with 75 lb of $ 12 type to get the required mixture.

Good Luck!!!

Answer by jai_kos(139) (Show Source): You can put this solution on YOUR website!
LEt the coffee merchant has x lb and y lb of the coffee beans
x + y =100
x* 9 +y * 12 = 11.25 * 100

We shallsolve the given equations
WE rewrite the equation(1) as
x = 100 - y -->(3)
Now substitue equation(3) in equation(2), we get
(100 - y) * 9 + y *12 = 11.25 * 100
900 - 9y + 12y = 1125
900 + 3y = 1125
3y = 1125 - 900 = 225
3y =225
Divide by 3 we get,
y = 225 / 3
y = 75 lb

Now substitue the "y" value in equation)3), we get
x = 100 - 75 = 25lb
Therefore the quantity of coffee beans of first type is 75lb and the second type is 25 lb

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