SOLUTION: a grocer wants to create a mixture of jolly ranchers and tootsie pops. if jolly ranchers sell for $2 per pound and tootsie pops sell for $5 per pound how many pounds of toosie pop

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: a grocer wants to create a mixture of jolly ranchers and tootsie pops. if jolly ranchers sell for $2 per pound and tootsie pops sell for $5 per pound how many pounds of toosie pop      Log On

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Question 1130954: a grocer wants to create a mixture of jolly ranchers and tootsie pops. if jolly ranchers sell for $2 per pound and tootsie pops sell for $5 per pound how many pounds of toosie pops must be mixed with 20 pounds of jolly ranchers to create a mixture that sells for $4 per pound?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
p, pounds of tootsie pops
20-p, pounds of jolly ranchers

cross%285p%2B2%2820-p%29=4%2A20%29
5p%2B2%2A20=4%28p%2B20%29
5p=4p%2B4%2A20-2%2A20
p=2%2A20
p=40

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The other tutor misread the problem. The equation they show is if the total weight of the jolly ranchers and tootsie pops is 20 pounds. The problem says there are 20 pounds of jolly ranchers and an unknown number of pounds of tootsie pops.

For the question as stated, then, the equation to solve has to say that the total value of 20 pounds of jolly ranchers at $2 per pound, plus x pounds of tootsie pops at $5 per pound, is equal to the value of (20+x) pounds of the mixture at $4 per pound:

2%2820%29%2B5%28x%29+=+4%2820%2Bx%29

You can solve the equation to find the answer to the problem.

Here is a very different way of solving "mixture" problems like this that will get you to the answer much faster if you understand it (and if an algebraic solution is not required).

(1) The $4 per pound cost of the mixture is "twice as close" to $5 (the cost per pound of the tootsie pops) as it is to $2 (the cost per pound of the jolly ranchers).
(2) Therefore, the number of pounds of tootsie pops must be twice the number of pounds of jolly ranchers.

ANSWER: The mixture needs 2*20 = 40 pounds of tootsie pops.