Question

For his coffee shop, Abdul wants to make a mocha-java blend that will sell for $18/kg. The mocha coffee beans sell for $20/kg, and the java coffee beans sell for $15/kg. How many kilograms of each kind of coffee bean should he use to make 50 kg of the mocha-java blend?

Answer 1

30 kg of mocha coffee bean and 20 kg of java coffee bean should be used to make 50 kg of mocha java blend that will sell for $ 18 per kg

Solution:

Let "x" be the kilogram of mocha coffee beans

Let "y" be the kilogram of java coffee beans

Cost of 1 kg of mocha coffee bean = $ 20

Cost of 1 kg of java coffee bean = $ 15

Kilograms of each kind of coffee bean should he use to make 50 kg of the mocha-java blend

Cost of 1 kg of mocha java blend = $ 18

From given information,

Mocha coffee beans and java coffee beans are mixed to get 50 kg of blend

Therefore,

$x + y = 50 ------------ eqn 1$

Abdul wants to make a mocha-java blend that will sell for $18/kg

Therefore, we frame a equation as:

(kilogram of mocha coffee beans) x (Cost of 1 kg of mocha coffee bean) + (kilogram of java coffee beans) x (Cost of 1 kg of java coffee bean) = Cost of 1 kg of mocha java blend x 50 kg

Thus we get,

$x \times 20 + y \times 15 = 18 \times 50\\\\20x+15y = 900 ------------ eqn 2$

Let us solve eqn 1 and eqn 2

From eqn 1,

x = 50 - y -------- eqn 3

Substitute eqn 3 in eqn 2

20(50 - y) + 15y = 900

1000 - 20y + 15y = 900

5y = 100

y = 20

Substitute y = 20 in eqn 3

x = 50 - 20

x = 30

Thus 30 kg of mocha coffee bean and 20 kg of java coffee bean should be used to make 50 kg of mocha java blend that will sell for $ 18 per kg