A girl has X number of cherries. She eats 1 and then gives her sister 1/2 of those left. She eats another cherry and then gives her brother 1/3 of what is left over. The girl now has 6 cherries. What is the number of cherries with which she began?
+130511 Let x be the number she started with
Then
(x - 1) - (1/2)(x - 1) - 1 - (1/3)[(x-1) - (1/2)(x-1) -1] = 6 simplify
x -1 - (1/2)x + 1/2 - 1 - (1/3)x + (1/3) + (1/6)x - (1/6) +1/3 = 6
x - (5/6)x + (1/6)x - 2 +1/2 +1/3 - 1/6 + 1/3 = 6
(1/3)x - 1 = 6 add 1 to both sides
(1/3)x = 7 multiply both sides by 3
x = 21
Check
21 - 1 = 20
Then 20 - (1/2)(21 - 1) = 20 - 10 = 10 to her sister
Then 10 - 1 = 9
And 9 - (1/3)(9) = 9 - [3 to her brother] = 6 (√√√)
+130511 Let x be the number she started with
Then
(x - 1) - (1/2)(x - 1) - 1 - (1/3)[(x-1) - (1/2)(x-1) -1] = 6 simplify
x -1 - (1/2)x + 1/2 - 1 - (1/3)x + (1/3) + (1/6)x - (1/6) +1/3 = 6
x - (5/6)x + (1/6)x - 2 +1/2 +1/3 - 1/6 + 1/3 = 6
(1/3)x - 1 = 6 add 1 to both sides
(1/3)x = 7 multiply both sides by 3
x = 21
Check
21 - 1 = 20
Then 20 - (1/2)(21 - 1) = 20 - 10 = 10 to her sister
Then 10 - 1 = 9
And 9 - (1/3)(9) = 9 - [3 to her brother] = 6 (√√√)
