Question 1185586: A coffee company wants a new flavor of Cajun coffee. How many pounds of coffee worth $7 a pound should be added to 30 pounds of coffee worth $3 a pound to get a mixture worth $5 a​ pound?
Answer by ikleyn(52794)   (Show Source):
You can put this solution on YOUR website! .
Let "p" be the pounds added.
Then you have this money equation
7p + 3*30 = 5*(30+p).
Simplify and find p
7p + 90 = 150 + 5p
7p - 5p = 150 - 90
2p = 60
p = 60/2 = 30.
ANSWER. 30 pounds should be added.
CHECK. The ingredients cost, in total, 7*30 + 3*30 = 210 + 90 = 300 dollars.
The mixture costs 5*(30+30) = 5*60 = 300 dollars. ! Correct !
Solved.
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You may notice that the numbers $3, $5 and $7 dollars make a remarkable sequence: the middle $5 is midway between $3 and $7.
Therefore, you may expect that the amounts of the ingredients to mix are the same: 30 pounds.
It is the way how to guess the answer MENTALLY, without making calculations.
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