Question

Brown's Grounds Coffee is selling for $2.50 a pound is mixed with Coffee From Heaven selling for $2.80 a pound to produce 100 pounds of a blend selling for $2.62 per pound. How many pounds of each kind of coffee were mixed?

Answer 1

Answer: the number of pounds of Brown's Grounds Coffee that was mixed is 60

the number of pounds of Coffee From Heaven that was mixed is 40

Step-by-step explanation:

Let x represent the number of pounds of Brown's Grounds Coffee that was mixed.

Let y represent the number of pounds of Coffee From Heaven that was mixed.

Brown's Grounds Coffee is selling for $2.50 a pound is mixed with Coffee From Heaven selling for $2.80. 100 pounds was produced and sold at the rate of $2.62 per pound. This means that the total cost of the blend produced is 100×2.62 = $262. Therefore

2.5x + 2.8y = 262 - - - - - -- - -- - -1

x + y = 100

Substituting x = 100 - y into equation 1, it becomes

2.5(100 - y) + 2.8y = 262

250 - 2.5y + 2.8y = 262

- 2.5y + 2.8y = 262 - 250

0.3y = 12

y = 12/0.3 = 40

x = 100 - y = 100 - 40

x = 60