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I need to prepare a number of questions for my homework on numbers and fractions. Not being a native English speaker, I'm stuck on constructing a question.

Everyday a student solves questions in the following manner:

1st day: n questions
2nd day: n + ${n\over5}$ questions=k questions
3rd day: k + ${k\over5}$ questions=m questions
4th day: m + ${m\over5}$ questions

The question:

(This is the part I'm stuck)
If on the 4th day she solves 648 questions, how many questions did she solve on the 1st day?

(The answer is 375.)

The question shouldn't involve any unknowns, only the numbers ${1\over5}$ and 648.

W.R.P.S
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martavallo
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    Well, every day he solves $20%$ more questions than the day before that and on the fourth day he solved $648$ questions. If you say that, you won't have any unknowns or anything. The only thing is that you use percentages instead of fractions. is that a problem for you? – Mastrem Dec 28 '16 at 21:07
  • @Mastrem Can you please use 1/5? – martavallo Dec 28 '16 at 21:09
  • 20% is equivalent to 1/5. 0.2 * 5 = 1, thus 2/10 (or 0.2) is 1/5. Does that help clarify things? –  Dec 28 '16 at 21:13
  • @floorcat Thank you. I know they are equivalent, but I must use the fraction 1/5. – martavallo Dec 28 '16 at 21:18
  • How about this:

    "Each day a student answers 1/5 more homework questions than she did the day before, so if on the first day she answers 25 questions, then on the second day she will answer 30 questions. Suppose that on the 4th day, she answers 648 questions. How many did she answer on the first day?"

     – John Hughes Dec 28 '16 at 21:19
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    @martavallo "Can you please use 1/5 (instead of 20%)...I know they are equivalent, but I must use the fraction 1/5" That sounds to me like if you were asked to use the number $\color{red}{3}$ and you are complaining that you aren't allowed to use $\color{blue}{3}$ because the color is incorrect despite the value and the meaning being exactly the same... – JMoravitz Dec 28 '16 at 21:25
  • @John Hughes Thank you. If the example part "so if on the first day she answers 25 questions, then on the second day she will answer 30 questions" is omitted, will the question still be understandable? – martavallo Dec 28 '16 at 21:26
  • It'll probably still be comprehensible, but the exact meaning of "1/5 more" could be confusing to some readers, so the illustrating example is helpful. – John Hughes Dec 28 '16 at 22:11
  • I wrote it as an answer to your question, if the answer solves your problem I would appreciate you accepting it as the answer. :) –  Dec 28 '16 at 22:15
  • @John Hughes It was the use of "more" in such a context that had troubled me for hours. Because the question in my own language is unambiguously clear and I didn't use example, I'll first submit it without the example and wait for the reaction of the supervisor. Thank you very much for your kindness. – martavallo Dec 28 '16 at 22:41
  • What is the grade level of the students? It's hard to know what is an appropriate formulation of the problem without knowing who the students are. – mweiss Dec 28 '16 at 23:36

1 Answers1

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A student is solving an unlimited supply of problems.

Each day after the first day, the total number of problems solved increases by an amount equal to $\frac{1}{5}$ of the amount of solved problems from the day before.

If by the fourth day the total number of solved problems is $648$, how many problems were solved on the first day?

JMoravitz
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  • I think this is too wordy for the level of education the students are at. –  Dec 28 '16 at 22:49