In a certain candy store, 3 pounds of candy and 2 pounds of mints cost $10.80, and 1 pound of candy and 3 pounds of mints cost $5.35. What is the cost per pound of the mints?

The trick with these question to 'get rid of 1 of the unknowns so that you can solve for the remaining one.

Let the cost of candy per pound be #c#
Let the cost of mints per pound be #m#

Then we have:

#3c+2m=$10.80#.............................(1)
#c+3m=$5.35#....................................(2)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider equation(2)

#" "color(brown)(c+3m=5.35)#

Subtract #color(blue)(3m)# from both sides

#" "color(brown)(c+3mcolor(blue)(-3m)=5.35color(blue)(-3m))#

But #3m-3m=0#

#" "c+0=5.35-3m#

#" "c=5.35-3m...........................(2_a)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute #(2_a)# into (1)

#color(brown)(3c+2m=$10.80)color(blue)(" "->" "3(5.35-3m)+2m=10.8#

#" "16.05-9m+2m=10.8#

#" "16.05-7m=10.8#

#" "7m=16.05-10.8#

#" "7m=5.25 larr" note that 5.25 is " 5 1/4#

#" " m= 1/(cancel(7)^1)xx(cancel(21)^3)/4 = #

#" "m=3/4#
.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(green)("I will let you solve for the cost of candy")#

Hint: substitute #m=3/4# in one of the original equations