Lời giải:
Ta có: $\frac{31-n}{43-n}=\frac{3}{5}$
$\frac{5\times (31-n)}{5\times (43-n)}=\frac{3\times (43-n)}{5\times (43-n)}$
$5\times (31-n)=3\times (43-n)$
$5\times 31-5\times n=3\times 43-3\times n$
$155-5\times n=129-3\times n$
$155-5\times n-(129-3\times n)=0$
$155-5\times n-129+3\times n=0$
$(155-129)-(5\times n-3\times n)=0$
$26-2\times n=0$
$2\times n=26$
$n=13$
Theo đề, ta có:
\(\dfrac{31-n}{43-n}=\dfrac{3}{5}\)
\(\Leftrightarrow155-5n=129-3n\)
\(\Leftrightarrow-2n=-26\)
hay n=13