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 ?

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) (Show Source): You can put this solution on YOUR website!
The ratio A:B is 2:3. We can rewrite this as .
Multiplying both sides by b gives . This is our first equation.

If you add 100 to each, we get .
Multiplying both sides by 4 gives .
Multiplying both sides by (100+b) gives .
Distributing gives .
Now we can substitute into this equation to get .
Simplifying this gives .
Subtracting 300 from both sides gives .
Since 3 = 9/3, we can rewrite this as .
Subtracting from both sides gives .
Multiplying both sides by 3 gives .
Since , we can plug in b=300 to get .
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.
RELATED QUESTIONS
Can anyone please help me make sense of this?? Thank you so much for your time!... (answered by stanbon)

1)The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In (answered by mananth)

Q: If a, b and y are positive real numbers with such that none of them is equal to 1 and... (answered by Boreal)

If a, b, and c are numbers such that a/b = 3 and b/c = 7, then a+b/b+c is equal to... (answered by ewatrrr)

Which of the following statements is false? A. Any two numbers, a and b, have a sum,... (answered by Alan3354)

The numerator and denominator of a fraction are in a ratio 2:3. If 8 is added to both... (answered by mananth)

Explain how complex numbers combine under the following operations: a. Addition... (answered by lynnlo)

The conversion rate of our website is 2.5%, meaning that from 1000 website visitors 25... (answered by CPhill)

Dear Sir I would be glad if you can help me to resolve the below problems that has been (answered by ankor@dixie-net.com)