The secretary spent her 35 hour work week in this manner: 1/5 of her time sorting mail, 1/7 of her time filing

Question

The secretary spent her 35 hour work week in this manner: 1/5 of her time sorting mail, 1/7 of her time filing letters, and ½ of her time typing. The rest of her time she acted as a receptionist. The percentage of her time spent as a receptionist during the week was most nearly

Answer 1

1 - 1/7 - 1/5 - 1/2
= 11/70 = 15.7%

Answer 2

The amount of time she spent working as a receptionist is:

(1 - 1/5 - 1/7 - 1/2)*35 = [(70 - 14 - 10 - 35)/70]*35

= (11/70)*35 = 11/2 = 5 1/2 hours

Answer 3

Convert each fraction to a number of hours. For example, if she spent one fifth of 35 hours sorting mail, she must have spent 7 hours sorting mail.

It comes out like this:

7 hrs sorting mail
5 hrs filing
17.5 hrs typing

Subtract all these numbers from the total, 35 hours:

35 - (7+5+17.5) =

35 - 29.5 = 5.5 hours

So, the percentage of time is the fraction made by this number divided by the total, 35, and then multiplied by 100:

(5.5 / 35) x 100 = 15.7 %

So she spent 15.7 % of her time as a receptionist.

Answer 4

note
1/5 + 1/7 = 7/35 + 5/35 = 12/35
add 1/2
12/35 + 1/2 = 24/70 + 35/70 = 59/70
59/70 = .842857 or approx 84.3% of her time doing other things
so 15.7% of her time was spent as a receptionist

Answer 5

sorting mail = 7 hours
filing letters = 5 hours
typing = 17.5 hours => 50%

receptionist = 35 - 29.5 (add the rest) = 5.5 hours => about 15.71 % of the time