Finding c knowing $c = 3k + 2$, $c = 4l + 3$ and $100 \leq c \leq 110$

Question

I need to model and solve the problem with a diophantine equation. As title says, the things I know are: \begin{align*} c &= 3k + 2 \\ c &= 4l + 3 & \text{and } 100 \leq c \leq 110 \\ \end{align*}

Edit: I've found that the result is 107, because:

$$26\cdot 4 + 3 = 107$$ and $$35\cdot 3+2=107$$

but I'm still not able to recognize how to model it with a diophantine equation.

Answer 1

solving your Diophanine equation $$3k-4l=1$$ we get $$k=3+4m,l=2+3m$$ where $m$ is an arbitrary integer number. Can you finish now?