The average time a man spent watching TV daily for the past week is 4 hours. if we remove one of these days, the average time he spent watching TV is now 3.5. How many hours of TV time did the man have on the day we removed?
Answers
Answer:
5 hours was removed
Step-by-step explanation:
4 hours in the past week, 5 hours each time in the past week he watched tv.
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He spent 7 hrs on the day we removed
Given:
The average of time a man watching TV daily for the past week is 4 hours
When we remove one of these days, the average time he spent watching TV is now 3.5
To find:
How many hours of TV time did the man have on the day we removed?
Solution:
Number of days in week = 7 days
Let x₁, x₂, x₃, x₄, x₅, x₆ and x₇ be hr of time spent by man for 7 days
Given that the average of time a man watching TV a week = 4 hrs
As we know
Average = (Sum of hrs spent on each day) ÷ 7
= (x₁+x₂+x₃+x₄+x₅+x₆+x₇)/ 7
From given data Average time spent for week = 4 hrs
⇒ (x₁+x₂+x₃+x₄+x₅+x₆+x₇)/ 7 = 4
⇒ x₁+x₂+x₃+x₄+x₅+x₆+x₇ = 28 -------(1)
From given data Average after removing one = 3.5 hrs
Let's assume that the last day x₇ is removed
Then average of x₁, x₂, x₃, x₄, x₅, x₆ will be
= (x₁+x₂+x₃+x₄+x₅+x₆)/6
From given data
⇒ (x₁+x₂+x₃+x₄+x₅+x₆)/6 = 3.5
⇒ x₁+x₂+x₃+x₄+x₅+x₆ = 21 -----(2)
Now substitute (2) in (1)
⇒ x₁+x₂+x₃+x₄+x₅+x₆+x₇ = 28
⇒ 21 + x₇ = 28
⇒ x₇ = 28 - 21 = 7
Therefore, He spent 7 hrs on the day we removed
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