A numismatist decides to divide their coin collection between their children.
The eldest gets 1/2 of the collection, the next gets 1/4, the next gets 1/5, and the youngest gets the remaining 49 coins.
How many coins are in the collection?
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What do the fractions add to?
There are 980 coins in the collection.
To check this we add:
1÷2 + 1÷4 + 1÷5 + 49
this works out as
490 + 245 + 196 + 49 = 980, as required.
To work the answer out from the question, we observe that:
1÷2 + 1÷4 + 1÷5 = 19÷20
and we know that there were 49 coins left, so 1÷20 of the collection is 49 coins.
This means that the entire collection is 20 x 49 = 980 coins.
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