SOLUTION: Please help me with some word problems. I have tried for several hours and cant figure out where to begin. A coffee maker wants to make a coffee blend by mixing two different c

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Question 153484: Please help me with some word problems. I have tried for several hours and cant figure out where to begin.
A coffee maker wants to make a coffee blend by mixing two different coffee beans. Colombian coffee is $3 per pound, while Costa Rican coffee is $6 per pound. The company wants 90 pounds of this mixture which will sell for $4 per pound. How many pounds of each type of coffee should be used?

Thank you.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Colombian $3.00/lb, let's use C as the number of pounds of Colombian.
Costa Rica $6.00/lb, let's use R as the number of pounds of Costa Rican.
We want a total 90 pounds so we know,
1.C%2BR=90
We also want to sell it for $4.00/lb.
The average price will be cost of the Colombian plus the cost of the Costa Rican divided by the total number of pounds.
2.%283C%2B6R%29%2F%28C%2BR%29=4
From 1, we can substitute into 2,
2.%283C%2B6R%29%2F%28C%2BR%29=4
2.%283C%2B6R%29%2F90=4
2.3C%2B6R=360
Use eq. 1 to solve for C in terms of R.
1.C%2BR=90
C=90-R
Now substittue that expression into eq. 2 and solve for R.
2.3C%2B6R=360
3%2890-R%29%2B6R=360
270-3R%2B6R=360
3R=90
highlight%28R=30%29
From above,
C=90-R
C=90-30
highlight%28C=60%29
Let's check the per pound price to verify the answer.
3C%2B6R=360
3%2860%29%2B6%2830%29=360
180%2B180=360
360=360
True, good answer.
60 pounds Colombian, 30 pounds Costa Rican.