Andy & Jack each have a number of candies. Andy gives 1/2 of his candies to Jack. After that Jack gives 1/3 of his candies to Andy. At last both of them have 20 candies each. How many candies did Andy have at first?
original:
Andy ---- a
Jack ----- j
after first give-away:
Andy ---- a/2
Jack ----- j + a/2
after 2nd give-away:
Jack --- (2/3)(j + a/2)
Andy ---- a/2 + (1/3)(j+a/2)
(2/3)(j + a/2) = 20
2(j + a/2) = 60
2j + a = 60 ***
a/2 + (1/3)(j+a/2) = 20
times 6
3a + 2(j + a/2) = 120
3a + 2j + a = 120
4a + 2j = 120 **
subtract *** from **
3a = 60
a = 20
in *** 2j + 20 = 60
j = 20