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?

Answer 1

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