Question

A variety of candies costing $10.50 per kg is mixed with another variety costing $15 per kg, to make a mixture of 12kg that would cost $12.50 per kg. how many kg of each variety were mixed?

Answer 1

`6 2/3` kgm of $10.50 candies, and
`5 1/3` kgm of $15.00 candies

Explanation:

Define
`color(white)("XX")m =`weight of $10.50 candies (in kgm)
`color(white)("XX")n =`weight of $15.00 candies (in kgm)

We are told
[1]`color(white)("XX")m+n=12`

and `color(white)("XX")10.50m+15.00n=12.50*12`
which simplifies to:
[2]`color(white)("XX")7m+10n = 100`

Multiplying [1] by 7
[3]`color(white)("XX")7m+7n=84`

Subtracting [3] from [2]
[4]`color(white)("XX")3n=16`

Dividing by 3
[5]`color(white)("XX")n=16/3=5 1/3`

Substituting `5 1/3` for `n` in [1] (and simplifying)
[6]`color(white)("XX")m=6 2/3`