Question 1108035: Donna wants to make trail mix made up of almonds, walnuts, and raisins. She wants to mix one part almonds, two parts walnuts, and three parts raisins. Almonds cost $12 per pound, walnuts cost $9 per pound, and raisins cost $5 per pound.
Donna has $15 to spend on the trail mix. Determine how many pounds of trail mix she can make. ( have an algebraic solution)
Found 4 solutions by mananth, ikleyn, josgarithmetic, n2:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! Donna wants to make trail mix made up of almonds, walnuts, and raisins. She wants to mix one part almonds, two parts walnuts, and three parts raisins. Almonds cost $12 per pound, walnuts cost $9 per pound, and raisins cost $5 per pound.
Donna has $15 to spend on the trail mix. Determine how many pounds of trail mix she can make. ( have an algebraic solution)
almonds, walnuts, and raisins.
Let quantity of trail mix she can make be x
1/12 part of x is almonds @ $12 per pound
2/12 part of x is walnuts @ $9 per pound
3/12 part of x is raisins @ $ 5 per pound
Cost of all three is $15
12(x/12) +9( x/6) +5( x/4) = 15
x+ 3x/2 + 5x/4 = 15
LCM
4x+6x+5x= 60
15x = 60
x =4
4 pounds of trail mix can be made by her
Answer by ikleyn(53619)  (Show Source):
You can put this solution on YOUR website! .
Donna wants to make trail mix made up of almonds, walnuts, and raisins. She wants to mix one part almonds,
two parts walnuts, and three parts raisins. Almonds cost $12 per pound, walnuts cost $9 per pound,
and raisins cost $5 per pound.
Donna has $15 to spend on the trail mix. Determine how many pounds of trail mix she can make. (have an algebraic solution)
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Setup equation in the post by @mananth is incorrect, leading to incorrect answer of 4 pounds of trail mix.
So, his solution is incorrect both technically and conceptually.
In my post below, I will give simple and short straightforward solution.
Let's combine 1 pound of almonds, 2 pounds of walnuts, and 3 pounds of raisins.
This combination is the prescribed proportion. The total mass of this mixture is 1 + 2 + 3 = 6 pounds,
and its total cost is 1*$12 + 2*$9 + 3*$5 = $45.
So, 6 pounds of this mixture cost 45 dollars.
$15 dollars that Donna has is 1/3 of $45 - - - hence,
for $15 Donna may have 1/3 of 6 pounds, i.e. 2 pounds of the mixture.
ANSWER. For $15, Donna may have 2 pounds of the mix.
Solved correctly.
Answer by josgarithmetic(39736)  (Show Source):
Answer by n2(55) (Show Source):
You can put this solution on YOUR website! .
Donna wants to make trail mix made up of almonds, walnuts, and raisins. She wants to mix one part almonds,
two parts walnuts, and three parts raisins. Almonds cost $12 per pound, walnuts cost $9 per pound,
and raisins cost $5 per pound.
Donna has $15 to spend on the trail mix. Determine how many pounds of trail mix she can make. (have an algebraic solution)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let's combine 1 pound of almonds, 2 pounds of walnuts, and 3 pounds of raisins.
This combination is the prescribed proportion. The total mass of this mixture is 1 + 2 + 3 = 6 pounds,
and its total cost is 1*$12 + 2*$9 + 3*$5 = $45.
So, 6 pounds of this mixture cost 45 dollars.
$15 dollars that Donna has is 1/3 of $45 - - - hence,
for $15 Donna may have 1/3 of 6 pounds, i.e. 2 pounds of the mixture.
ANSWER. For $15, Donna may have 2 pounds of the mix.
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