Percentages question for a 10 year old

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apple2357

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A friend has sent me this problem as he is struggling with this 10 year old who plans on sitting an entrance exam for a school.

12388

I can only do it using venn diagram and some clever algebra and have got an answer of 150. Can anyone offer an easier approach?
 
Here's one way to think through it:

If you add up 20%, 40%, and 60%, you get 120%. But that percentage counts twice those who learn two languages (and would count three times those who learn all three, if there had been any). Since 50% learn two languages, we can subtract that from the 120% to remove the double counting. That leaves 70% who learn at least one language, and 30% who learn none. Finally, 30% of 500 is 150, so that's the answer.

This reasoning is hidden behind MarkFL's work.
 
Dr.Peterson said:
Here's one way to think through it:

If you add up 20%, 40%, and 60%, you get 120%. But that percentage counts twice those who learn two languages (and would count three times those who learn all three, if there had been any). Since 50% learn two languages, we can subtract that from the 120% to remove the double counting. That leaves 70% who learn at least one language, and 30% who learn none. Finally, 30% of 500 is 150, so that's the answer.

This reasoning is hidden behind MarkFL's work.
Click to expand...

Thank you, i was just about to ask about MarkFL's reasoning! Makes sense - thank you.
 
Sorry, that was exactly my reasoning, and I thought it evident from the mathematical statement I posted. :)
 
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