Question

Chris bought some gum for 10 cents each and some candy for 15 cents each. the amount of candy was 12 less than three times the amount of gum. he spent a total of $2.10. how much of each did he buy? (you'll need to round the pieces of gum to the nearest whole number.) define the variables:

Answer 1

7 pieces of gum
9 pieces of candy

For this problem, I'll use the variable "c" for candy and "g" for gum. So let's create the equations to solve.
"the amount of candy was 12 less than three times the amount of gum"
c = 3g - 12 "

gum for 10 cents each...candy for 15 cents each ... he spent a total of $2.10" 0.10g + 0.15c = 2.10

Since we have an equation that expresses c in terms of g, let's substitute that for c in the 2nd equation and solve for g:
0.10g + 0.15c = 2.10
0.10g + 0.15(3g - 12) = 2.10
0.10g + 0.45g - 1.80 = 2.10
0.55g - 1.80 = 2.10
0.55g = 3.90
g = 7.09090909
g = 7 (after rounded as problem specifies)

c = 3g - 12
c = 3*7 - 12
c = 21 - 12
c = 9

g * 0.10 + c * 0.15
= 7 * 0.10 + 9 * 0.15
= 0.70 + 1.35
= 2.05

I will assume the difference of $0.05 is for tax.