SOLUTION: A and B are whole numbers so that theratio A:B is equal to 2:3. if you add 100 to each of A and B, the new ratio becomes equal to 3:4. what is A ?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A and B are whole numbers so that theratio A:B is equal to 2:3. if you add 100 to each of A and B, the new ratio becomes equal to 3:4. what is A ?      Log On


   

Question 316218: A and B are whole numbers so that theratio A:B is equal to 2:3. if you add 100 to each of A and B, the new ratio becomes equal to 3:4. what is A ?
Answer by moshiz08(60) About Me  (Show Source):
You can put this solution on YOUR website!
The ratio A:B is 2:3. We can rewrite this as a%2Fb=2%2F3.
Multiplying both sides by b gives a=%282%2F3%29+b. This is our first equation.

If you add 100 to each, we get %28100%2Ba%29%2F%28100%2Bb%29=3%2F4.
Multiplying both sides by 4 gives +%28%28100%2Ba%29%2F%28100%2Bb%29%29+4+=+3+.
Multiplying both sides by (100+b) gives +%28100%2Ba%294+=+3%28100%2Bb%29+.
Distributing gives 400+%2B+4a+=+300+%2B+3b.
Now we can substitute a+=+%282%2F3%29+b into this equation to get 400+%2B+4%28%282%2F3%29+b%29+=+300+%2B+3b.
Simplifying this gives 400+%2B+%288%2F3%29+b+=+300+%2B+3b.
Subtracting 300 from both sides gives 100+%2B+%288%2F3%29+b+=+3b.
Since 3 = 9/3, we can rewrite this as 100+%2B+%288%2F3%29+b+=+%289%2F3%29+b+.
Subtracting %288%2F3%29+b from both sides gives 100+=+%281%2F3%29+b.
Multiplying both sides by 3 gives +300+=+b+.
Since a=%282%2F3%29+b, we can plug in b=300 to get a+=+%282%2F3%29+b+=+%282%2F3%29+%28300%29+=+200.
Now we check: the ratio of a=200 to b=300 is indeed 2:3. If we add 100 to both, we get the ratio (200+100)=300 to (300+100)=400, which is 300:400 which is 3:4 just as we wanted.