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,
[tex]x + y = 50 ------------ eqn 1[/tex]
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,
[tex]x \times 20 + y \times 15 = 18 \times 50\\\\20x+15y = 900 ------------ eqn 2[/tex]
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
