Question

Buckstars sells two types of coffee: one that costs $5.00 per pound and another that costs $6.20 per pound. How many pounds of the $5.00 per pound coffee should be mixed in with the $6.20 per pound coffee in order to have 30 pounds of a blend worth $5.50?

Answer 1

Suppose we use x pounds of the $5.00 coffee and y pounds of the $6.20 coffee.
Then we set up a system of 2 equations. We know we want a total of 30 lb, so:
x+y = 30
We also know we want the resulting coffee to cost $5.50 per pound, so the proportion of $5.00 to $6.20 coffee should allow for this. The coffee will be made up of x/30 of the $5.00 coffee and y/30 of the $6.20 coffee:
x/30 * 5.00 + y/30 * 6.20 = 5.50

Solve the system:
x+y = 30
x/30 * 5 + y/30 * 6.2 = 5.5

x = 30 - y
5x + 6.2y = 165
5(30-y) + 6.2y = 165
150 - 5y + 6.2y = 165
1.2y + 150 = 165
1.2y = 15
y = 12.5

x+y = 30
x + 12.5 = 30
x = 17.5

We can check this by plugging the numbers into the equations:

x+y = 30
17.5 + 12.5 = 30
GOOD

x/30*5 + y/30*6.2 = 5.5
17.5/30 * 5 + 12.5/30 * 6.2 = 5.5
2.9166666 + 2.58333333 = 5.5
GOOD