My watch keeps track of the number of active calories I burn each day. My weekly mean daily calories burned by Saturday last week was 1004. However by Sunday night, my weekly average ended up being 997 and I was disappointed not to keep average above 1000. How could I have calculated what total I needed on Sunday to keep average calories burned above 1000 for the week?
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2$\begingroup$ (1) How many calories had you burned by Saturday night? (2) How many did you want to burn for the week ending Sunday night? (3) Subtract. $\endgroup$– whuber ♦Commented May 8, 2017 at 19:13
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1 Answer
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Suppose you want to burn at least an average of $y$ calories per day in $N$ days, and after $k$ days you burned an average of $x$ calories per day (where $k<N$). Then you want to burn an average of $z$ calories per day in the remaining $N-k$ days such that, $$ \frac{k x + (N-k) z}{N} \ge y, $$ which can be rearranged to give $$ z \ge\frac{N y - k x}{N-k}. $$
In your specific case, $k=6,$ $N=7,$ $x=1004,$ and $y=1000.$
