Question 208660
Well this is a system of 3 equations with 3 unknowns. Now we assign variables to our unknowns.  Let c = time spent making calls, e = time spent writing emails, and m = time spent in meetings.  Well then we know that she worked 7.5 hours that day.  So our first equation will be c + e + m = 7.5.  Next we know that she spent twice as much time attending meetings as making calls.  In an equation this would be 2c = m.  Next we know that she spent 1/2 hour longer writing emails then making calls.  so we know that 1/2+c = e.  <br>

So our system is:<br>

c + e + m = 7.5
2c = m
1/2 + c = e<br>

SO since m and e are both in terms of c then we can plug in for e and m in equation 1 and solve for c.<br>

c + e + m = 7.5
c + 1/2 + c + 2c = 7.5
4c + 1/2 = 15/2
4c = 14/2 = 7
c = 7/4 = 1.75<br>

so we know that she spent 1.75 hours making calls<br>

now we can plug that in to the other two equations and solve for m and e.<br>

2c = m 
2(7/4) = m
7/2 = m = 3.5<br>

so she spent 3 and a half hours in meetings.<br>

e = c + 1/2
e = 7/4 + 1/2
e = 9/4 = 2.25<br>

so she spent 2.25 hours in meetings. <br>

and if you add them up 9/4 + 7/2 + 7/4 = 9/4 + 14/4 + 7/4 = 30/4 = 7.5 hours so we did it right.