Amber coaches soccer and volleyball. She coaches both sports for a total of 7 hours each day. The soccer practice lasts 1 hour more than twice as long as the volleyball practice. Write a system of equations to model the situation. Use v for the number of hours Amber coaches volleyball in a day and s for the number of hours she coaches soccer.
Accepted Solution
A:
Amber coaches both sports for 7 hours each day
v = volleyball hours s = soccerball hours
7 hours in total, in which soccerball is 1 hour more than volleyball: v + s = 7 s = v + 1
plug in v + 1 for s
v + s = 7 v + (v + 1) = 7
simplify
v + v + 1 = 7 2v + 1 = 7 2v + 1 (-1) = 7 (-1) 2v = 6 2v/2 = 6/2 v = 6/2 v = 3
Plug in 3 for v for one of the equations.
s = v + 1 s = (3) + 1 s = 4
Amber coaches 3 hours for volleyball, and 4 hours for soccer, making a total of 7 hours