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.