A coin collector decides to divide his coin collection between his children.
The eldest gets 1/2 of the collection, the next gets 1/4 of the collection, the next gets 1/5 of the collection, and the youngest gets the remaining 49 coins.
How many coins are in the collection?
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Hint
What do the fractions add up to?
Answer
There are 980 coins in the collection.
Reasoning
Using fractions:
1/2 + 1/4 + 1/5 = 19/20
The remaining 1/20 is 49 coins.
Therefore, the 20/20 must equal 20 lots of 49 = 980.
Alternative Reasoning
Using percentages:
50% + 25% + 20% = 95%
The remaining 5% is 49 coins.
If 5% is 49 coins, 10% is 98 coins, 100% is 980 coins.
Double-Checking
1/2 of 980 is 490
1/4 of 980 is 245
1/5 of 980 is 196
and the remaining 49 coins.
And 490 + 245 + 196 + 49 = 980.
