Math Is Fun Forum

Samanana

Guest

Need help with whole number sense

okay so ' how old are your three children?' Luciana asked her new neighbor, Benoit. 'their ages are positive integers, all different, whose product is 90'.
Benoit replied. 'and the sum of their ages is the number of my house.'
'Their ages are all more than the age of your youngest child.'
a) what is the number of Benoit's house?'

it would be great if someone could help me, Thanks!

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,045

Re: Need help with whole number sense

Benoit's house is numbered 14 or 16.
her three children are aged 3, 5, and 6 years or
2, 5 and 9 years.
When she says 'their ages are all more than the age of your youngest child',
it cannot be inferred what is the age of Luciana's youngest child. It could be 1 year or 2 years. Hence, there are two possibilities.

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Samanana

Guest

Re: Need help with whole number sense

Thanks for the help!

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Need help with whole number sense

The question is answerable if we assume that everything Benoit says is needed.
Here are the possible sets of ages (with their sums):

1 2 45 (48)
1 3 30 (34)
1 5 18 (24)
1 6 15 (22)
1 9 10 (20)
2 3 15 (20)
2 5 9   (16)
3 5 6   (14)

In most cases, knowing the product and sum of the ages would be enough, so the information about the youngest child would be unrequired.
The exception to this is when the house number is 20.

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Why did the vector cross the road?
It wanted to be normal.