how many poundsof nuts selling at 12 a pound and rasins at 6 pr pound should a person use to cvombine to obtain 90 lbs of a trail mix for 8 dollars per pound

Question

How many pounds of nuts selling for $12
per lb and raisins selling for $6
per lb should a person combine to obtain 90
lb of a trail mix selling for $8
per lb?

Answer 1

30 lbs of the $12 nuts + 60 lbs of the $6 raisins.  How come?

 

Alligation: tic-tac-toe method

 

HAVE........NEED.........WANT.....

$12.............................2.........

..................$8.......................

$6..............................4........

 

So, you need 2 PARTS of the $12 and 4 PARTs of the $6.  This adds to 6 parts, but the whole is 90 parts (pounds).

Thus, 90/6 = 15, so multiply each by 15 to get 2x15 = 30 pounds of the $12 and 4x15 = 60 pounds of the $6.

More traditional approach: x lbs($12) + Ylbs($6) = 90 lbs ($8) x + y = 90 x = 90-y (12)(90-y) + 6y = 720 6y = 360 y = 60 lbs of the $6 raisins x = 30 lbs of $12 nuts