# Question

(a)

If there were 27n pies initially, Adam ate 27n * 2/3  + 2/3 = 18n + 2/3

So the remaining pies were  27n – ( 18 n + 2/3) = 9n -2/3

Bryan ate (9n – 2/3 ) 2/3 + 2/3 = 6n – 4/9 + 6/9 = 6n + 2/9

So the remaining pies were 9n – 2/3 – ( 6n + 2/9) = 3n – 8/9

Finally,  Clara ate ( 3n – 8/9) 2/3 + 2/3 = 2n – 16/27 + 18/27 = 2n + 2/27

2n + 2/27 = 3n – 8/9

n = 2/27 + 24/27 = 26/27

So 27n = 26

Initially there were 26 pies.

(b)

Bryan eaten  6n + 2/3 = 6(26/27) + 2/9 = 54/9 = 6 pies

Sorry for making mistake on the answer, corrected.

0 Replies 1 Like ✔Accepted Answer

(a) Another solution by working backwards,

Clara eaten 2/3 of remaining and left with 1/3 which was 2/3 pie that she had eaten at last.

So the number of pies left before Clara started eating was 3* 2/3 = 2 pies.

So number of pies after Bryan eaten 2/3 of remaining pies = 2 2/3 pies or 8/3 pies.

Number of pies left before Bryan started eating =  3 * 8/3 = 8 pies.

So number of pies after Adam eaten 2/3 of remaining pies = 8 2/3 pies.or 26/3 pies.

Number of pies in the beginning = 3 * 26/3 = 26 pies.

(b) Bryan eaten 8 * 2/3 + 2/3 = 18/3 = 6 pies