Question

Your school's talent show will feature 10 solo acts and 3 ensemble acts. The show will last 99 minutes. The 5 solo performers judged best will give a

repeat performance at a second 69 minute show, which will also feature the 3 ensemble acts. Each solo act lasts x minutes, and each ensemble act
lasts y minutes. Use this information to answer parts (a) and (b).
a) Write a system of equations to model the situation.
A.3x + 10y = 69 3x + 5y = 99
B.10x + 3y = 99 5x + 3y = 69
C.10x + 3y = 6 5x + 3y = 99
D.3x + 10y = 99 3x + 5y = 69

Answer 1

To model the situation, set up a system of equations using x for solo act minutes and y for ensemble act minutes. The correct equations are 3x + 10y = 69 and 3x + 5y = 99.

Step-by-step explanation:

To model the situation, we can set up a system of equations based on the given information. Let's let x represent the number of minutes each solo act lasts, and y represent the number of minutes each ensemble act lasts.

For the first show, we know that there are 10 solo acts and 3 ensemble acts, and the show lasts 99 minutes. This can be represented by the equation 10x + 3y = 99.

For the second show, the 5 solo performers judged best will give a repeat performance, along with the 3 ensemble acts. The second show lasts 69 minutes. Since there are only 5 solo acts in the second show, the equation becomes 5x + 3y = 69.

Therefore, the correct system of equations to model the situation is option A: 3x + 10y = 69 and 3x + 5y = 99.