SOLUTION: The manager of a coffee shop has one type of coffee that sells for $6 per pound and another type that sells for $15 per pound. The manager wishes to mix 70 pounds of the $15 coffee

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Question 725032: The manager of a coffee shop has one type of coffee that sells for $6 per pound and another type that sells for $15 per pound. The manager wishes to mix 70 pounds of the $15 coffee to get a mixture that will sell for $12 per pound. How many pounds of the $6 coffee should be used?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
ASSIGN VARIABLES
u= UNKNOWN, how many pounds of $6/pound coffee
v= 70, the number of pounds of $15/pound coffee
L= $6/pound
H= $15/pound
T= $12/pound WANTED

WRITE EQUATIONS FOR THE SITUATION
highlight%28%28uL%2BvH%29%2F%28u%2Bv%29=T%29
Solve for u, and then substitute known or given values to evaluate.

SOLVING FOR u
uL%2BvH=T%28u%2Bv%29
uL%2BvH=Tu%2BTv
uL-Tu=-vH%2BTv
u%28L-T%29=Tv-vH
u%28L-T%29=v%28T-H%29, multiply both members by (-1) because of the order of L, T, and H
u%28T-L%29=v%28H-T%29
highlight%28u=v%28H-T%29%2F%28T-L%29%29, the formula for u.

SUBSTITUTE VALUES
The final computation using the known or given values is left undone, for you to do.