Wiskundeleraar

moet ik dit kunnen snappen?

Gegeven is de formule $N=\frac{{\Large20k + 30}}{{\Large4m + 1}}$

Neem $m=1$ en druk $N$ uit in $k$.
Neem $k$=4. Voor welke $m$ is $N=11$?
Neem $N=5$ en schrijf $m$ in de vorm $m = ak + b$.

$
\begin{array}{l}
N = \frac{{\Large20k + 30}}{{\Large4 \cdot 1 + 1}} \\
N = \frac{{\Large20k + 30}}{{\Large4 + 1}} \\
N = \frac{{\Large20k + 30}}{\Large5} \\
N = \frac{{\Large20k}}{\Large5} + \frac{{\Large30}}{\Large5} \\
N = 4k + 6 \\
\end{array}
$

$
\begin{array}{l}
11 = \frac{{\Large20 \cdot 4 + 30}}{{\Large4m + 1}} \\
11 = \frac{{\Large80 + 30}}{{\Large4m + 1}} \\
11 = \frac{{\Large110}}{{\Large4m + 1}} \\
11(4m + 1) = 110 \\
4m + 1 = 10 \\
4m = 9 \\
m = 2\frac{1}{4} \\
\end{array}
$

$
\begin{array}{l}
5 = \frac{{\Large20k + 30}}{{\Large4m + 1}} \\
5(4m + 1) = 20k + 30 \\
20m + 5 = 20k + 30 \\
20m = 20k + 25 \\
m = k + 1\frac{1}{4} \\
\end{array}
$