SOLUTION: Hi the ratio of bobs cards to gregs cards was 3:4.after bob bought 12 cards and greg lost 24 cards the ratio became 3:2 what was the total number of cards bob and greg had at f

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Hi the ratio of bobs cards to gregs cards was 3:4.after bob bought 12 cards and greg lost 24 cards the ratio became 3:2 what was the total number of cards bob and greg had at f      Log On


   



Question 942174: Hi
the ratio of bobs cards to gregs cards was 3:4.after bob bought 12 cards and greg lost 24 cards the
ratio became 3:2 what was the total number of cards bob and greg had at first.
thank you

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the ratio of bobs cards x to gregs cards y was 3%3A4
x%3Ay=3%3A4............eq.1
after bob bought 12 cards and greg lost 24 cards the
ratio became 3%3A2
%28x%2B12%29%3A%28y-24%29=3%3A2............eq.2
x%3Ay=3%3A4............eq.1
4x=3y
y=4x%2F3


%28x%2B12%29%3A%28y-24%29=3%3A2............eq.2
2%28x%2B12%29=3%28y-24%29
2x%2B24=3y-72..........plug in y=4x%2F3

2x%2B24=3%284x%2F3%29-72
2x%2B24=4x-72 ......solve for x
72%2B24=4x-2x
96=2x
x=48
and y=4x%2F3 => y=%284%2A48%29%2F3 => y=64
the total number of cards Bob had at first 48
and Greg had at first 64