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?

Puzzle Copyright © Kevin Stone

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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.