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?

1 Answer
Sep 7, 2015

Answer:

#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#