Question

Tammy's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Tammy $4.55 per pound, and type B coffee costs $5.65 per pound. This month, Tammy made 160 pounds of the blend, for a total cost of $807.20 . How many pounds of type A coffee did she use?

Answer 1

x=pounds of Type A coffee
y=pounds of Type B coffee


QUANTITY EQUATION:
x+y=160

COST EQUATION:
$4.55x + $5.65y=$807.20

STEP 1:
Solve for one variable in equation one. Then substitute it in equation two.

x+y=160
subtract y from both sides of the equation
x=160-y


STEP 2:
substitute x=160-y in equation two

$4.55x + $5.65y=$807.20
4.55(160-y) + 5.65y=807.20
multiply 4.55 by everything in parentheses

(4.55*160)+(4.55*-y)+5.65y=807.20
728-4.55y+5.65y=807.20
combine like terms

728+1.10y=807.20
subtract 728 from both sides

1.10y=79.20
divide both sides by 1.10

y=72 pounds of type B coffee


STEP 3:
Substitute y=72 in either equation to solve for x

x+y=160
x+72=160
subtract 72 from both sides
x=88 pounds of type A coffee


ANSWER:
x=88 pounds of type A coffee
y= 72 pounds of type B coffee


CHECK:
Substitute answers for x & y into either equation to be sure it checks.

4.55x + $5.65y=$807.20
4.55(88)+5.65(72)=807.20
400.40+406.70=807.20
807.20=807.20

Hope this helps! :)