SOLUTION: I'm am really not sure where to begin to solve this problem. I know that I should set one side of the equation to 6 1/2. The question is: In her Job at the post office, Janie wo

Question 1051628: I'm am really not sure where to begin to solve this problem. I know that I should set one side of the equation to 6 1/2. The question is:
In her Job at the post office, Janie works a 6 1/2 hour day. She sorts mail, sells stamps, and does supervisory work. On one day, she sold stamps twice as long as she sorted mail, and sold stamps 1 hour longer that the time she spent doing supervisory work. How many hours did she spend at each task?
Found 2 solutions by Boreal, josmiceli:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
sell stamps=x hours
sorted mail is 1/2*x, half as long
supervisory work is x-1
They add to 6.5
x+0.5x+x-1=6.5
2.5x-1=6.5
2.5x=7.5
x=3 hours (sell stamps)
sorted mail is 1.5 hours, or half of 3.
supervisory work was 2 hours, or x-1
They add to 6.5 hours
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
There are 3 unknowns:
(1) Number of hrs spent sorting mail =
(2) Number of hrs spent selling stamps =
(3) Number of hrs spent doing supervisory work =
---------------------
You need 3 equation in order to find 3 unknowns
given:
(1)
(2)
(3)
----------------------
(2)
and
(3)
Substitute 92) and (3) into (1)
(1)
(1)
Multiply both sides by
(1)
(1)
(1)
and
(2)
(2)
and
(3)
(3)
(3)
---------------------
She spent 1.5 hrs sorting mail,
3 hrs selling stamps, and 2 hrs
doing supervisory work
------------------------------
check:
(1)
(1)
(1)
You can check (2) and (3)

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