Find the number of pounds of each to be used in the mixture.

Question

A gift store is making a mixture of almonds, pecans, and peanuts, which sell for 6.50 per pound, 8.00 per pound and 4.00 per pound respectively. The store-keeper wants to make 20 pounds of the mix to sell at 5.30 per pound. The number of pounds of peanuts is to be three times the number of pounds of pecans. Find the number of pounds of each to be used in the mixture.

Answer 1

almonds = X

pecans = Y

peanuts = Z

 

X + Y + Z = 20

 

Z = 3Y

 

6.5X + 8Y + 4Z = 20*5.3

 

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substitutes Z=3y into the first and third equations

and then simplifies

 

X+4y = 20   --->  x = 20 - 4y

6.5X + 20Y = 106

 

6.5(20 - 4y) + 20 y = 106

 

130 - 26y + 20y = 106

130 - 6y = 106

-6y = -24

y = 4

z=12

x=4