Question

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.

Answer 1

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

hope this helps

Answer 2

Answer:

v=2 s=5

Step-by-step explanation:

a) v=volleyball s=soccer

s × v = 7

" the soccer (s) practice lasts 1 hour (1) more than (+) twice as long (2) as the volleyball (v) practice; this simplifies to: s = 1 + 2v

b) substitute equation for soccer for s

(1 + 2v) + v = 7

solve for v

1 + 3v = 7   (2v + v = 3v; that's where the 3v comes from)

we subtract 1 from both sides

3v = 6

we divide 3 from both sides

v=2

solve for s

since we know what v equals, we substitute it in

s + 2 =7

subtract 2 from both sides

s = 5