SOLUTION: Andy, Bernard and Cassandra shared a number of sweets in the ratio 3:7:5. Andy gave {{{1/6}}} of his sweets to Bernard. Bernard then gave {{{7/15}}} of his sweets to Cassandra. C

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Andy, Bernard and Cassandra shared a number of sweets in the ratio 3:7:5. Andy gave {{{1/6}}} of his sweets to Bernard. Bernard then gave {{{7/15}}} of his sweets to Cassandra. C      Log On


   

Question 1184634: Andy, Bernard and Cassandra shared a number of sweets in the ratio 3:7:5. Andy
gave 1%2F6 of his sweets to Bernard. Bernard then gave 7%2F15 of his sweets to Cassandra.
Cassandra then gave 30 of her sweets to Andy. If the ratio of the number of sweets
Andy had to the number of sweets Bernard had to the number of sweets Cassandra
had in the end was 5:4:6, how many sweets did each person have at first?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!



                                              Andy  Bernard  Cassandra

                                            ----------------------------

At the start, the ratio A:B:C was 3:7:5        3x      7x      5x

Andy gave 1/6 of his (0.5x) to Bernard        2.5x    7.5x     5x

Bernard gave 7/15 of his (3.5x) to Cassandra  2.5x     4x     8.5x

Cassandra gave 30 of hers to Andy             2.5x+30  4x    8.5x-30



The ratio of Andy to Bernard in the end was 5:4

%282.5x%2B30%29%2F%284x%29=5%2F4

2.5x%2B30=5x

2.5x=30

x=12



ANSWERS:

Andy to start: 3x=36

Bernard to start: 7x=84

Cassandra to start: 5x=60

CHECK:

Andy at end: 2.5x+30=60

Bernard at end: 4x=48

Cassandra at end: 8.5x-30=72



A:B:C at end: 60:48:72=5:4:6