Math problem?

Your school's talent show will feature 10 solo acts and 2 ensemble acts. The show will last 82 minutes. The 5 solo performers judged best will give a repeat performance at a second 52  minute show, which will also feature the 2 ensemble acts. Each solo act lasts x minutes, and each ensemble act lasts y minutes.

Solve the system from part (a).

1 Answer
May 1, 2018

The solution is #x = 6 and y = 11#.

Explanation:

#10x + 2y = 82#
#5x + 2y = 52#

Subtracting the 2nd equation from the first, we get:
#5x = 30#
#implies x = 30/5 = 6#

Substituting x = 6 in equation 2, we get:
#5xx6 + 2y = 52#
#implies2y= 52 - 30#
#implies y = 22/2 = 11#