Value mixture problem using linear equations

Question

The coffee shop has 2 types of coffee. A cost 5.65 per lb and B costs 4.55 per lb.this months blend uses 4 times as many pounds of type B then type A for a total cost of 620.10

Answer 1

For two unkown variables, you need two equations:

let A = the number of lbs of coffee A

let B = the number of lbs of coffee B

there are 4 times as many pounds of B than A, therefore our first equation is B=4A

in total, the coffee shop spends 620.1, therefore our second equation is 5.65A + 4.55B = 620.1

set up a system of equations, and substitute B=4A into the second equation to get 5.65A + 4.55(4A) = 620.1

solve for A. A = 23.85 lbs

use the first equation, B = 4A to solve for B

B = 4(23.85)

B = 95.4 lbs