SOLUTION: Cashew nuts are sold at $15.00/kg. Walnuts are sold at $12.00/kg. What quantities of each nut would a store owner put into 100-kg barrel so that it could be sold for $13.20/kg?

Algebra ->  Linear-equations -> SOLUTION: Cashew nuts are sold at $15.00/kg. Walnuts are sold at $12.00/kg. What quantities of each nut would a store owner put into 100-kg barrel so that it could be sold for $13.20/kg?      Log On


   

Question 1105613: Cashew nuts are sold at $15.00/kg. Walnuts are sold at $12.00/kg. What quantities of each nut would a store owner put into 100-kg barrel so that it could be sold for $13.20/kg?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
A very routine mixture exercise question.

x of $15/kg cashews
100-x of $12/kg walnuts

15x%2B12%28100-x%29=13.20%2A100
Find x and evaluate 100-x.

STEPS
15x%2B1200-12x=100%2813.20%29
3x%2B1200=100%2813.20%29
3x=%2813.2%29%28100%29-%2812%29%28100%29
3x=%281.2%29%28100%29
3x=120
highlight%28x=40%29-----------kilograms of the cashews, $15 per kg

100-x=highlight%2860%29--------kilograms of the walnuts, $12 per kg

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


Think of the three per-pound prices on a number line: $12, $13.20, and $15.

The price for the mixture, $13.20, is 40% of the way from $12 to $15:
13.20-12+=+1.20; 15-12+=+3; 1.20%2F3+=+.40 = 40%.

That means 40% of the mixture should be the $15 per pound cashews.

40% of 100kg is 40kg.

The store owner should use 60kg of walnuts and 40kg of cashews.

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Here is another variation of the same method for finding the answer.

matrix%283%2C3%2C12%2C%22%22%2C1.80%2C%22%22%2C13.20%2C%22%22%2C15%2C%22%22%2C1.20%29

In this chart, the $12 and $15 per kg prices are in the first column and the $13.20 per kg price of the mixture is in the second column. Then the numbers in the third column are the differences, calculated diagonally, between the numbers in the first and second columns: 13.20-12 = 1.20; 15-13.20 = 1.80.

When the numbers are used this way, the 1.80 and 1.20 are the ratio in which the $12 per pound walnuts and $15 per pound cashews should be mixed.
1.80%3A1.20+=+3%3A2, so the nuts should be mixed 3 parts walnuts to 2 parts cashews.

3 parts to 2 with a total of 100kg means 60kg of walnuts and 40kg of cashews.