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. (3 points) (a) 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. (b) how many hours each day does amber spend coaching each sport?

answer(a):

let number of hours amber coaches volleyball in a day = v

let number of hours amber coaches soccer in a day = s

then total number of coaching hours = s+v

given that she teaches for 7 hours each day so we get equation

s+v=7

or

s=7-)

given that soccer practice lasts 1 hour more than twice as long as the volleyball practice. so we get equation:

s=2v+)

hence required system of equation is given by {s=7-v, s=2v+1}

answer(b):

now set both equations equal to each other:

2v+1=7-v

2v+v=7-1

3v=6

divide both side by 3

v=2

now plug value of v=2 into (i)

s=7-v=7-2=5

hence number of hours amber coaches volleyball in a day = 2

and number of hours amber coaches soccer in a day = 5

answer rather than having to add and subtract the measurements of the semi-circle, notice that the semicircle to the left of ad is actually identical in area to the blank semicircle-shaped space to the left of bc. so if we transferred the red semicircle into the blank space, we would end up with a square of side length 24 cm. the area of a square is s^2 = 24^2 = 676 cm^2.

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