U2.L3.HW: Systems of Linear Equations: Question 30

Question

A coffee distributor plans to mix some Kenya coffee that normally sells for $13.20 per pound with some Guatemala Antiguacoffee that normally sells for $14.20 per pound to create 60 pounds of a new coffee blend that can sell for $13.93 per pound. How many pounds of each kind of coffee should they mix?

Answer 1

Let x = number of pounds of Kenya coffee

Let y = number of pounds of Guatemala coffee

Write two equations. One that represents how many pounds of coffee are used. The number of pounds of Kenya plus the number of pounds of Guatemala equals 60.

x + y = 60

The second equation is about the value of the coffee.

Each pound of Kenya coffee is worth $13.20 or 13.2x.

Each pound of Gautemala coffee is worth $14.20 or 14.2y.

Each pound of the mixture is worth $13.93 and there are 60 pounds or 13.93 x 60 = $835.80.

Value of Kenya coffee plus value of Guatemala coffee is worth $835.80.

13.2x + 14.2y = 835.8

Put these two equations together as a system of equations.

x + y = 60

13.2 x + 14.2y = 835.8

To solve by Elimination, you could multiply the first equation by -13.2 so that the coefficients of the x terms become opposites. Distribute -13.2 times each of the three terms.

-13.2 ( x + y = 60)

-13.2x - 13.2y = -792

Combine this with the second equation. Add straight down.

-13.2x - 13.2y = -792

+ 13.2 x + 14.2y = 835.8

y = 43.8

Substitute this value into the the original first equation

x + y = 60

x + 43.8 = 60

Subtract 43.8 from both sides.

x = 16.2

So you need 16.2 pounds of Kenya coffee and 43.8 pounds of Guatemala coffee.