Kelly blends coffee. She mixes brand A costing $6 per kg with brand B costing $8 per kg. How many kilograms of each brand does she have to mix to make 50 kg of coffee costing her $7.20 per kg?

1 Answer
Oct 11, 2017

#20#kg of brand A, #30#kg of brand B

Explanation:

This is a system of equations problem. Let's first define the variables.

Let #x# be the kg of coffee of brand A in the mix and #y# be the kg of coffee of brand B in the mix.

The total kg must be #50#.

#x+y=50#

The cost per kg of the mix must br #$7.20#. For this, the total cost of the mix will be #6x+8y#, so the total cost per kg of the mix will be #(6x+8y)/50#.

#(6x+8y)/50=7.20#

Now that we have our two equations, we can solve.

#6x+8y=7.20*50#

#6x+8y=360#

From the first equation, we can multiply both sides by #6# to get:
#6x+6y=300#

Subtracting, we get:

#2y=60#

#y=30#

Thus, we need #30# kg of brand B in our mix. This means that #50-30=20# kg will be of brand A.