SOLUTION: 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 aâ

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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(52798)   (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.

---------------

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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