Question

A coffee distributor needs to mix a(n) Queen City coffee blend that normally sells for $11.90 per pound with a Arabian Mocha coffee blend that normally sells for $13.10 per pound to create 10 pounds of a coffee that can sell for $12.86 per pound. How many pounds of each kind of coffee should they mix? A) Write an equation using the information as it is given above that can be solved to answer the question. Use x as your variable to represent the quantity of Queen City coffee blend. Equation: B) Answer: They must mix pounds of the Queen City Blend pounds of the Arabian Mocha Blend. Round your answers to the nearest whole number of pounds.

Answer 1

The variables are:

x: quantity of Queen City coffee blend, in pounds

y: quantity of Arabian Mocha coffee blend, in pounds

10 pounds of a coffee are needed, then:

x + y = 10 (eq. 1)

Queen City coffee is sold for $11.90 per pound, Arabian Mocha coffee is sold for $13.10 per pound, the blend must be sold for $12.86 per pound, then:

11.9x + 13.1y = 12.86*10

11.9x + 13.1y = 128.6 (eq. 2)

Isolating x from the first equation:

x = 10 - y

Substituting the last equation into the second equation:

11.9(10 - y) + 13.1y = 128.6

11.9*10 - 11.9y + 13.1y = 128.6

119 + 1.2y = 128.6

1.2y = 128.6 - 119

1.2y = 9.6

y = 9.6/1.2

y = 8

And the value of x is:

x = 10 - 8

x = 2

They must mix 2 pounds of the Queen City Blend and 8 pounds of the Arabian Mocha Blend.