Mixture of a 38% mix and a 62% mix to form a 50% mix of a 144 lbs bag.

Question

A trail mix is comprised of 38% raisins is being mixed with a trail mix variety that is 62% Raisins to create a 144 lbs of trail mix that is 50% raisin. How many pounds of the 38% raisin trail mix must be used?

Answer 1

The problem can be expressed as two equations in two unknowns.

 

X = first trail mix in pounds

Y = second trail mix in pounds

 

1)The 38% trail mix is mixed with the 62% trail mix to produce a 50% trail mix of 144 lbs.

2)The weight of the two trail mixes adds to 144 lbs.

 

1) 0.38X + 0.62Y = 0.50(144)

2)       X  +   Y     = 144

 

multiply equation 2 by 0.62, then subtract equation 2 from equation 1.

 

1) 0.38X + 0.62Y = 0.50(144)

2)- 0.62(X  + Y)      = -0.62(144)

 

0.38X - 0.62X = 0.50(144) - 0.62(144)

-0.24X = -0.12(144)

X = 0.12(144)/0.24 = 72 lbs.