Question

Campos is mixing Kona beans and Maui beans to make 25 pounds of coffee blend. Kona beans cost Campos $15 per pound and Maui beans cost $24 per pound. How many pounds of each coffee bean should Campos use for his blend to cost him $17.70 per pound?

Answer 1

Campos should use 17.5 pounds of Kona beans and 7.5 Maui beans

Step-by-step explanation:

The sum of Kona and Maui beans = 25 pounds

Kona + Maui = 25 Pounds

let number of Kona beans = a

number of Maui beans = 25 - a

The cost of Kona beans per pound = $15

Total cost of a number of Kona beans = a × $15 = 15a

The cost of Maui beans per pound = $24

Total cost of Maui beans = 24 × (25 - a)

Amount of coffee blend = 25 pound

Cost of coffee blend per pound = $17.70

Total cost of 25 pound coffee bleend = 25 × 17.7

The equation:

Total cost of a number of Kona beans + Total cost of Maui beans = Total cost of 25 pound coffee blend

15a + 24 × (25 - a) = 25 × 17.7

15a + 600 - 24a = 442.5

collect like terms:

15a - 24a = 442.5 - 600

-9a = -157.5

Divide both sides by -9:

-9a/-9a = -157.5/-9

a = 17.5

Kona beans = 17.5 pounds

Maui beans = 25 - 17.5 = 7.5

Hence, Campos should use 17.5 pounds of Kona beans and 7.5 Maui beans