> when a is divided by b the quotient is 7 and the remainder is 8.

This is equivalent to

- a = 7b + 8. [Eq. 1]

You’re also told:

- a - b = 74. [Eq. 2]

These are two linear equations in two unknowns. Solving them simultaneously (either by substitution or elimination) is fairly straightforward. My first step would be to rearrange Eq. 2 as

- a = b + 74

and then eliminate a by combining the two equations.

Does that help?