solving a value mixture problem using a linear equation

Question

Ivan's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Ivan
$5.80
per pound, and type B coffee costs
$4.55
per pound. This month, Ivan made
128
pounds of the blend, for a total cost of
$652.40
. How many pounds of type A coffee did he use?

Answer 1

 

(x lbs)($5.80) + (128 lbs - x lbs)($4.55) = $652.40

5.80x + 582.40 - 4.55x = 652.40

1.25x = 70

x = 56 lbs A

Answer 2

let type a cofee = x pounds and type b cofee = y pounds

 

x+y=128

5.8x+4.55y=652.4

 

x=56  ans

y=72