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?

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(39626)   (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

Simplify and solve.
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
let = pounds of granola needed
Let = pounds of nuts needed
-----------------
(1)
(2)
-----------------------------------
(2)
Multiply both sides of (1) by and
subtract (1) from (2)
(2)
(1)
---------------------------

and

-----------------
3.6 pounds of granola and 5.4 pounds of nuts are needed
check:
(2)
(2)
(2)
(2)
(2)
OK
Answer by greenestamps(13203)   (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.
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