Question 516258: I have already finished 26 problems, this is the last one on my assignment and I'm stuck, please help. Twenty pounds of trail mix are made by mixing 10 pounds of raisins worth $3 per pound with peanuts worth $4 per pound and M&M's worth $5 per pound. How many pounds of peanuts must be used if the mixture is to be worth $3.79 per pound?
Found 2 solutions by mananth, solver91311:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Twenty pounds of trail mix are made by mixing 10 pounds of raisins worth $3 per pound with peanuts worth $4 per pound and M&M's worth $5 per pound. How many pounds of peanuts must be used if the mixture is to be worth $3.79 per pound?
raisins-----------10---------------3
peanuts-----------x---------------4
M&M--------------(20-(10+x))-------5
Mixture-----------20-------------3.79
10*3+4*x+5(10-x)=20*3.79
30+4x+50-5x=75.8
-x=75.8-80
x= 4.2 pounds peanuts
M&M=>(10-4.2)=5.8 pounds
m.ananth@hotmail.ca
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
Notice that we want to end up with 20 lbs of mix, half of which is raisins and the other half is a mix of nuts and M&Ms. So the cost of the 10 lbs of raisins and the cost of the 10 lbs of nuts/M&Ms mix has to average (because the amounts are the same) to $3.79.
So the first question is "What is the cost of the nut/M&M mix that averages with $3.00/lb to make $3.79? When you average two numbers, you add them together and divide by 2. The result of that calculation was $3.79, so 2 times $3.79 is $7.58. Subtract $3.00 to get $4.58 which must be the cost of the nut/M&M mix. Like Dr. Livingstone said: Safari, so goodie.
Now, let  represent the number of lbs of peanuts required. Then, since the peanuts and the M&Ms must weigh 10 lbs when all is said and done,  must be the weight of the M&Ms.
The cost of lbs of peanuts is then  dollars and the cost of lbs of M&Ms is then ) dollars. When you add up these two costs, you get 10 lbs times 4.58 per pound equals $45.80. Symbolically:
\ =\ 45.80)
All that you have to do now is solve for , the number of lbs of peanuts.
John
My calculator said it, I believe it, that settles it
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