Answer:
A=65, B=40
Step-by-step explanation:
The problem can be rewritten by using the following equations:
[tex]A-B=25\\\frac{A}{B}=\frac{13}{8}[/tex]
where the second equation means "A:B is equivalent to 13:8".
The second equation can be rewritten as:
[tex]8A=13B[/tex]
Which means
[tex]A=\frac{13}{8}B[/tex]
Substituting this into the first equation, we get
[tex]A-B=25\\\frac{13}{8}B-B=25\\\frac{13}{8}B-\frac{8}{8}B=25\\\frac{5}{8}B=25\\\\\frac{1}{8}B=5\\B=40[/tex]
And by susbtituting B=40 into the first equation, we find
[tex]A=\frac{13}{8}B=\frac{13}{8}(40)=13 \cdot 5=65[/tex]
So, the solution is
A=65
B=40
