intermediate algebra

Question

A coffee merchant combines coffee that costs $5 per pound with coffee that costs $4.10 per pound. How many pounds of each should be used to make 27 lb of a blend costing $4.75 per pound? 

$5 per lb coffee ?

$4.10 per lb coffee?

Answer 1

a + b = 27

5a + 4.1b = 4.75(27)

a = 27 - b

5(27 - b) + 4.1b = 128.25

135 - 5b + 4.1b = 128.25

0.9b = 6.75

b = 7.5

a = 27 - 7.5

a = 19.5