Solving a value mixture problem using a linear equation

Question

Pablo's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Pablo $5.80

per pound, and type B coffee costs $4.35

per pound. This month, Pablo made 143

pounds of the blend, for a total cost of $746.75

. How many pounds of type B coffee did he use?

Answer 1

A $5.80 per lb., B =$4.35 per lb.

mixed to get

143 lbs for $746.75

let x= lbs of A solve for 143-x

5.8x + 4.35(143-x) = 143(746.75)

1.365x = 143(746.75- 4.35) = 143(742.41)

expand, combine like terms, solve for x, then for 143-x = lbs of B

or

746.75/143= about average $5.222 per lb for the mix, very two-ish

5.8-5.22 = .58

5.2-4.35 = .85

A is closer price so more A than B

.85/.58 ratio = about 1.47

1.47 = x/(143-x)

cross multiply

143(1.47)- 1.47x = x

2.47x = 210.21

x = 210.21/2.47 = 85.1 lbs for A

143 -85.1 = 57.9 lbs for B