SOLUTION: Lauren works 7.5 hours a day. She spent the day making calls, emails, and meetings. She spent twice as much time attending meetings as making calls. She spent 0.5 hour longer wr

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Lauren works 7.5 hours a day. She spent the day making calls, emails, and meetings. She spent twice as much time attending meetings as making calls. She spent 0.5 hour longer wr      Log On


   

Question 208660: Lauren works 7.5 hours a day. She spent the day making calls, emails, and meetings. She spent twice as much time attending meetings as making calls. She spent 0.5 hour longer writing emails than making calls. How many hours did she spend on each task?
Answer by algebrapro18(249) About Me  (Show Source):
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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.

So our system is:

c + e + m = 7.5
2c = m
1/2 + c = e

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.

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

so we know that she spent 1.75 hours making calls

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

2c = m
2(7/4) = m
7/2 = m = 3.5

so she spent 3 and a half hours in meetings.

e = c + 1/2
e = 7/4 + 1/2
e = 9/4 = 2.25

so she spent 2.25 hours in meetings.

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.