SOLUTION: Granola costs $4.50 per pound. Assorted nuts cost $7 per pound. How many pounds of granola and nuts are needed to make 9 pounds of trail mix that costs $6 per pound?

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Question 1126100: Granola costs $4.50 per pound. Assorted nuts cost $7 per pound. How many pounds of granola and nuts are needed to make 9 pounds of trail mix that costs $6 per pound?
Found 3 solutions by josgarithmetic, josmiceli, greenestamps:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
This type been done already thousands of times.

Quick way using algebra,

x pounds of the nuts
9-x pounds of granola

4.5%289-x%29%2B7x=6%2A9
Simplify and solve.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
let +a+ = pounds of granola needed
Let +b+ = pounds of nuts needed
-----------------
(1) +a+%2B+b+=+9+
(2) +%28+4.5a+%2B+7b+%29+%2F+9+=+6+
-----------------------------------
(2) +9a+%2B+14b+=+108+
Multiply both sides of (1) by +9+ and
subtract (1) from (2)
(2) +9a+%2B+14b+=+108+
(1) +-9a+-+9b+=+-81+
---------------------------
+5b+=+27+
+b+=+5.4+
and
+a+%2B+5.4+=+9+
+a+=+3.6+
-----------------
3.6 pounds of granola and 5.4 pounds of nuts are needed
check:
(2) +%28+4.5a+%2B+7b+%29%2F9+=+6+
(2) +%28+4.5%2A3.6+%2B+7%2A5.4+%29%2F9+=+6+
(2) +%28+16.2+%2B+37.8+%29%2F+9+=+6+
(2) +54+=+6%2A9+
(2) +54+=+54+
OK

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


You have received one full algebraic solution and the setup for a similar algebraic solution for your problem; here is a method for solving this kind of problem that, if you understand it, will get you to the answer much faster.

(1) $6.00 is three-fifths of the way from $4.50 to $7.00. (do a little mental arithmetic....)

(2) Therefore, three-fifths of the mixture must be the $7 per pound nuts.

(3) 3/5 of the 9 pounds is 27/5 pounds, or 5.4 pounds.

So 5.4 pounds of the nuts and 9-5.4 = 3.6 pounds of the granola.