Thin Lenses Problem: Solving for $q=d-p$

[Archimedess]

Homework Statement

We try with a thin convergent lens, by moving it on its optical axis, to project on a fixed screen the image of a small object located in the optical axis. This is only possible with two position of the lens $I_1=20cm$ and $I_2=80cm$. Determine the $d$ distance from the object to the screen and focal length $f$ of the lens.

Relevant Equations

$\frac{1}{p}+\frac{1}{q}=\frac{1}{f}$
$d=q+p$

Where $p$ is the distance of the object from the lens and $q$ is the distance between the image and the lens.

Since $d=q+p \implies q=d-p$
\begin{cases}
\frac{1}{I_1}+\frac{1}{d-I_1}=\frac{1}{f}\\
\frac{1}{I_2}+\frac{1}{d-I_2}=\frac{1}{f}
\end{cases}

Is this correct?

 

[BvU]

Yes. Now manipulate until you have an expression for $d$.