Kenneth took out 2 more than 1/2 of the total number of photos in his album on Tuesday and took out 4 fewer than 1/3 of the remaining photos in his album. If there were 24 photos left in the album, how many photos were there at first?
x = number of photos
Kenneth took out 2 more than 1/2 of the total number of photos in his album means:
He took:
x / 2 + 2 photos
Remaining photos = x / 2 - 2
He took out 4 fewer than 1/3 of the remaining means, he took:
( x / 2 - 2 ) / 3 - 4
Totaly he took:
x / 2 + 2 + ( x / 2 - 2 ) / 3 - 4 =
x / 2 + ( x / 2 - 2 ) / 3 - 2 photos
Remaining =
x - [ x / 2 + ( x / 2 - 2 ) / 3 - 2 ] =
x - x / 2 - ( x / 2 - 2 ) / 3 + 2 =
x / 2 - ( x / 2 - 2 ) / 3 + 2
24 photos left means:
x / 2 - ( x / 2 - 2 ) / 3 + 2 = 24
Multiply both sides by 6.
3 x - 2 ( x / 2 - 2 ) + 12 = 144
x - 2 x / 2 + 4 + 12 = 144
3 x - x + 4 + 12 = 144
2 x + 16 = 144
Subtract 16 to both sides.
2 x = 128
x = 128 / 2
x = 64
At the beginning, he had 64 photos.
Check result.
Kenneth took out 2 more than 1 / 2 of the total number of photos.
He took 64 / 2 + 2 = 32 + 2 = 34 photos.
Remaining = 64 - 34 = 30 photos
Then he took 4 fewer than 1/3 of the remaining photos .
He took:
30 / 3 - 4 = 10 - 4 = 6 photos
30 - 6 = 24 photos left