Sophia did push-ups every day for 7 days. Each day after the first day, she did 5 more push-ups than the day before. In total she did 175 push-ups. How many push-ups did Sophia do on the last day?
, 2016
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Solution
Sophia did push-ups for 7 days (an odd number of days), and on each day she did an equal number of push-ups more than the day before (5 more).
Therefore, the number of push-ups that Sophia did on the middle day (day 4) is equal to the average number of push-ups that she completed each day.
Sophia did 175 push-ups in total over the 7 days, and thus on average she did push-ups each day.
Therefore, on day 4 Sophia did 25 push-ups, and so on day 5 she did push-ups, on day 6 she did push-ups and on the last day she did push-ups.
(Note: We can check that , as required.)
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