Question

Two whole numbers A and B satisfy the following conditions. Find A and B . A−B=25 A:B is equivalent to 13:8

Answer 1

A=65, B=40

Explanation:

The problem can be rewritten by using the following equations:

`A-B=25\\(A)/(B)=(13)/(8)`

where the second equation means "A:B is equivalent to 13:8".

The second equation can be rewritten as:

`8A=13B`

Which means

`A=(13)/(8)B`

Substituting this into the first equation, we get

`A-B=25\\(13)/(8)B-B=25\\(13)/(8)B-(8)/(8)B=25\\(5)/(8)B=25\\\\(1)/(8)B=5\\B=40`

And by susbtituting B=40 into the first equation, we find

`A=(13)/(8)B=(13)/(8)(40)=13 \cdot 5=65`

So, the solution is

A=65

B=40