How many cups of each size of lemonade did they sell?

Question

Jose and Nick decide to sell lemonade on a hot summer day. They're selling two sizes: a 25-cent cup and a smaller 10-cent cup. At the end of the day, they've made $8.45.

They count the number of empty cups remaining. They started out with equal numbers of large and small cups, but now have three more small cups than large. How many cups of each size of lemonade did they sell?

Answer 1

845 = 25L + 10S

originally L=S, but now S= 3+L left

S=L-3 sold

25L + 10(L-3) = 845

35L = 845 -300 = 875

L = 875/35 = 25 larger sold

S = L-3 = 22 smaller sold

25(25) + 10(22) = 625 + 220 = 825 = $8.25 total

Answer 2

845 = 25L + 10S

originally L=S, but now S= 3+L left

S=L-3 sold

25L + 10(L-3) = 845

35L = 845 -300 = 875

L = 875/35 = 25 larger sold

S = L-3 = 22 smaller sold

25(25) + 10(22) = 625 + 220 = 825 = $8.25 total

25 = original L = original S

3 more larger sold leaving

25 L sold and 22 S sold