30% of number A is 10 more than 20% of number B. 30% of number B is 35 more than 20% of number A. Find the numbers A and B.

Question

A=?  B=?

Answer 1

set up two equations

30%A=10+20%B

30%B=35+20%A

0.3A=10+0.2B

0.3B=35+0.2A

0.3A-0.2B=10

-0.2A+0.3B=35

multiply all terms in both equations by 10 to eliminate the decimals

3A-2B=100

-2A+3B=350

multiply the first equation by 2 and multiply the second equation by 3

6A-4B=200

-6A+9B=1050

add the equations

5B=1250

B=1250/5

B=250

using 3A-2B=100...

3A-2(250)=100

3A-500=100

3A=500+100

3A=600

A=600/3

A=200 and B=250