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# How many days in $w$ weeks and $w$ days?

Last updated date: 20th Jun 2024
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Hint: Use the knowledge that one week of a month consists of seven days. First calculate the number of days that are equal to ‘w’ weeks by using the above relation and then add ‘w’ more days to that number.

Complete step by step solution:
The question is asked to find the number of days that are equal to w weeks and w days. This means that we have to find the number of days that are present in w weeks plus w days. To solve the given question, we must have knowledge of the English calendar. We must know that a week consists of 7 days. Or we can also say that the time that is covered in an interval, which is equal to 7 days is called a week. This means that one week is equal to seven days.
I.e. $1week=7days$.

Now, multiply w on both the sides of the above equation.
This gives us that $(w)week=(7w)days$.
This means that ‘w’ weeks are equal to a time of seven times w days. Now, if we add ‘w’ more days to ‘w’ weeks then the time covered in ‘w’ weeks and ‘w’ days is equal to $(w)weeks+(w)days$. But we know that,
$(w)week=(7w)days$.
With this we get that,
$(w)weeks+(w)days=(7w)days+(w)days\\ \therefore (w)weeks+(w)days=(8w)days$.

Therefore, we found that there are ‘8w’ days in ‘w’ weeks and ‘8w’ days.

Note:Some students may misunderstand that the time of ‘8w’ days is equal to 8 weeks by thinking that w is representation for one week. If the question asked to find the number of hours in ‘w’ weeks and ‘w’ days, then we have to multiply the answer by 24 as one day is equal to 24 hours.