sarah and james are selling popcorn and cotton candy
let popcorn be p and cotton candy be c
sarah sold 3 bags of popcorn and a sticks of cotton candy for a total of $75
3 x p + 9 x c = 75
3p + 9c = 75
james sold 8 bags of popcorn and 5 sticks of candy for $67
8 x p + 5 x c = 67
8p + 5c = 67
we have two equations
3p + 9c = 75 --------- equation 1
8p + 5c = 67 --------- equation 2
we can solve this simultaneously by using elimination method
first thing is to eliminate the variable c
to do this we multiply equation 1 by 5 and equation 2 by 9
3p x 5 + 9c x 5 = 75 x 5
8p x 9 + 5c x 9 = 67 x 9
15p + 45c = 375 ----- equation 3
72p + 45c = 603 ------ equation 4
substract equation 4 from equation 3
15p - 72p + 45c - 45c =
-57p + 0 = -288
-57p = -288
divide both sides by -57
-57p/-57 = -288 /-57
p = 4
to find c substitute p = 4 in equation 1
3p + 9c = 75
3(4) + 9c = 75
12 + 9c = 75
collect the like terms
9c = 75 - 12
9c = 63
divide both sides by 9
9c / 9 = 63/9
c = 7
the cost of popcorn is $4 and cotton candy is $7