Answer
7 singing acts and
5 comedy acts
Work Step by Step
Step $1$
Write the system of equations.
Let x = number of singing acts, y = number of comedy acts.
There were 12 acts in total:
$\quad x+y=12$
The total length was 50 min$.\qquad 5x+3y=50$
Step $2$
Solve one of the equations for one of the variables.
$x+y=12\quad y=12-x$
Step $3$
Substitute $12-x$ for $y$ in the other equation and solve for $x$
$5x+3y=50$
$5x+3(12-x)=50\quad $... simplify
$ 5x+36-3x=50\quad$ ... subtract $36$
$2x=14\quad $... divide with 2
$x=7$
Step $4$
Substitute $7$ for $x$ in$\quad x+y=12 \quad $and solve for $y$.
$y+7=15$
$y=5$
Reverting back to the meaning of x and y,
there were 7 singing acts and
5 comedy acts.
Check:
Length of singing acts: $5\cdot 7=35$ min.
Length of comedy acts: $3\cdot 5=15$ min.
Total : 50 minutes.
