A coffee distributor needs to mix a (n) Breakfast coffee blend that normally sells for $12.00 per pound with a Queen City coffee blend that normally sells for $14.10 per pound to create 80 pounds of a coffee that can sell for $12.92 per pound. How many pounds of each kind of coffee should they mix

Question

Justus Campbell

Mathematics

2 May, 03:46

A coffee distributor needs to mix a (n) Breakfast coffee blend that normally sells for $12.00 per pound with a Queen City coffee blend that normally sells for $14.10 per pound to create 80 pounds of a coffee that can sell for $12.92 per pound. How many pounds of each kind of coffee should they mix

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Answers (1)

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Dominik · Answer 1

They should mix 49.95 pounds of Breakfast coffe and 35.05 pounds of Queen city coffe

Step-by-step explanation:

first we have to perform 2 equations one to represent the quantity of liters of coffee and another the price

b = liters of Breakfast coffe

q = liters of Queen city coffe

b + q = 80

b * 12.00 + q * 14.10 = 80 * 12.92

we solve for b in the first equation

b + q = 80

b = 80 - q

we replace b with (80 - q) in the second equation

b * 12.00 + q * 14.10 = 80 * 12.92

(80 - q) * 12.00 + q * 14.10 = 80 * 12.92

960 - 12q + 14.10q = 1033.6

-12q + 14.10q = 1033.6 - 960

2.10q = 73.6

q = 73.6/2.10

q = 35.05

we replace q with its value in the first equation

b = 80 - q

b = 80 - 35.05

b = 49.95

They should mix 49.95 pounds of Breakfast coffe and 35.05 pounds of Queen city coffe