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See I have a test combined from 3 segments. The first two are 15% each, and the third is 70%. I can't do the second part, so they told me the scores would be 20% and 80% instead.

Now, the scores I got are 15% out of 15, which is easy, but on the third I got 48% out of 70. How do I know how many percent that is from the ultimate 80%? Would love the help. Thanks in advance :)

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If I understand you correctly, you have a score of $100$% on the first segment and $48/70$ of $100$%, or $\frac{48}{70}\cdot 100$%, on the third. The new weighting gives you $20$% of that $100$ plus $80$% of the $\frac{48}{70}\cdot 100$%: $0.2\cdot 100 + 0.8 \left(\frac{48}{70}\cdot 100 \right) = 20+ \frac{384}{7}\approx 74.857\text{ %}\;.$

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    If your interpretation is correct (and presumably it is) then the question should be edited, because as it stands now it's misleading. OP wrote $15\%$ out of $15$, which is definitely different than $15$ out of $15$. EDIT: Sorry to bring it up after so much time, the question showed up in my feed and I didn't check.2015-09-11