Question

In a talent show of singing and comedy acts, singing acts are 5 minutes long and comedy acts are 3 minutes long. The show has 12 acts and lasts for 50 minutes. How many singing acts and comedy acts are in the show?

Answer 1

Answer:the number of singing acts is 7

the number of comedy acts is 5

Explanation:

Let x represent the number of singing acts in the talent show.

Let y represent the number of comedy acts in the talent show.

The total number of acts in the talent show is 12. This means that

x + y = 12

In the talent show of singing and comedy acts, singing acts are 5 minutes long and comedy acts are 3 minutes long. The show lasts for 50 minutes. This means that

5x + 3y = 50 - - - - - - - - - -1

Substituting x = 12 - y into equation 1, it becomes

5(12 - y) + 3y = 50

60 - 5y + 3y = 50

- 5y + 3y = 50 - 60

- 2y = - 10

y = - 10/-2 = 5

Substituting y = 5 into x = 12 - y, it becomes

x = 12 - 5 = 7

Answer 2

• 7 singing acts
• 5 comedy acts

Explanation:

If all were comedy acts, the 12 of them would take 36 minutes. To make the show last 14 minutes longer, there must be 7 singing acts, since each adds 2 more minutes to the show than does a comedy act.

There are 7 singing acts and 5 comedy acts in the show.

_____

If you need an equation, let s represent the number of singing acts. Then the show length is ...

5s +3(12 -s) = 50

2s + 36 = 50 . . . . . eliminate parentheses

2s = 14 . . . . . . . . . . subtract 36 (the time for 12 comedy acts)

s = 7 . . . . . . . . . . . . divide by 2. This is the number of singing acts.

12 -s = 5 . . . . . . . . . the rest of the acts are comedy acts