# Math Help - I have a question.

1. ## I have several questions.

a is positive integer and b<13,

$\dfrac{a.b-b}{a}=7$

What is biggest value of b?

2. Originally Posted by OPETH
a is positive integer and b<13,

$\dfrac{a.b-b}{a}=7$

What is biggest value of b?
$\frac{ab-b}{a}=7$ re-arranges into $b = \frac{7a}{a-1}$.

The graph of b versus a is a hyperbola. Draw a graph and you'll see that the largest value of b that satisfies b < 13 and a is a positive integer is b = 21/2 corresponding to a = 3.

3. $b = \frac{7a}{a-1}$

and

if a=8

$b = \frac{7.8}{8-1}$ ,

$b = \frac{56}{7}$

$b = 8$

Thank you help.

4. Originally Posted by OPETH
$b = \frac{7a}{a-1}$

and

if a=8

$b = \frac{7.8}{8-1}$ ,

$b = \frac{56}{7}$

$b = 8$

Thank you help.
So b was also required to be an integer ....

5. $a.b-c=4$

$b.c-a=3$

in equality, a, b, c are positive integers.

What is total of $a+b+c$ minumum?

6. Originally Posted by OPETH
$a.b-c=4$

$b.c-a=3$

in equality, a, b, c are positive integers.

What is total of $a+b+c$ minumum?