Question

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?

Answer 1

`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.