Solving a value mixture problem using a linear equation

Question

Problem Page
Heather's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Heather
$5.50
per pound, and type B coffee costs
$4.25
per pound. This month's blend used three times as many pounds of type B coffee as type A, for a total cost of
$401.50
. How many pounds of type A coffee were used?

Answer 1

b = 3a

5.5a + 4.25b = 401.5

 

Substitute!

 

5.5a + 4.25(3a) = 401.5

5.5a + 12.75a = 401.5

18.25a = 401.5

a = 22