Jaclyn and Karen each bought some candies for their classmates. Each of them took out the same number of candies to distribute to their classmates. Jaclyn took out 2/3 of the candies from her bag and gave 7 candies to each of her classmates. She had 9 candies left over in her hands. Karen took out 3/4 of the candies from her bag and gave each of her classmates 10 candies. She was short of 18 candies in the end. How many candies did each girl bring to school at first?
number of classmates besides J and K ---- x
number of candies brought be each of J and K ----- m
J: 7(x+1) + 9 = (2/3)m
7x + 16 = 2m/3
21x + 48 = 2m , #1
K: 10(x+1) - 18 = (3/4)m
10x - 8 = 3m/4 ,
40x - 32 = 3m #2
#1 times 3 -----> 63x + 144 = 6m
#2 times 2 -----> 80x - 128 = 6m
then
80x - 128 = 63x + 144
17x = 272
x = 16
then in #1,
2m = 21(16) + 48
m = 192
each brought 192 candies