TinaSh
  • TinaSh
A mathematician states that her children’s ages are all prime numbers that multiply together to give 7,429. She also says that two of her children are teenagers. What are her children s age?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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freckles
  • freckles
so we have \[a \cdot b \cdot c=7429\]
freckles
  • freckles
we know prime numbers are odd for the most part
freckles
  • freckles
and we know 7429 is not even so none of the primes are 2

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freckles
  • freckles
two of her children are teenagers so they could be 13,17, or 19
freckles
  • freckles
I would probably try to write the prime factorization of 7429
freckles
  • freckles
can you do that?
TinaSh
  • TinaSh
wait what are prime numbers? :$
freckles
  • freckles
prime numbers are integers that are only divisible by themselves and 1.
freckles
  • freckles
the key here is just to write 7429 in prime factorization that is all there is to the problem
freckles
  • freckles
like for example 25=5*5 or 5^2 31 is prime 25 was not umm... 2 is the only even prime
TinaSh
  • TinaSh
I dont even know what factorization means >.< I missed few days of school.
campbell_st
  • campbell_st
one tip... given the last digit is 9... I'd divide the original number by 17
freckles
  • freckles
example: the prime factorization of 12=2*2*3
TinaSh
  • TinaSh
thanks <3
campbell_st
  • campbell_st
then see if the other 2 primes in the teens divides evenly
TinaSh
  • TinaSh
I don't know , I will try to figure it out thanks though
freckles
  • freckles
well the key to help was the teenager part
TinaSh
  • TinaSh
yeah , teens
freckles
  • freckles
"so they could be 13,17, or 19" exactly two of these numbers will be factors
freckles
  • freckles
then you have to find the other factor by divide 7429 by the product of two teenagers
freckles
  • freckles
what is 7429 divided by 13 ?
TinaSh
  • TinaSh
2476.3
freckles
  • freckles
you should get some kind of remainder that isn't 0 which would mean 13 is not factor of 7429 which means the other two number 17 and 19 are factors of 7429
freckles
  • freckles
so you only have to find one last factor
freckles
  • freckles
\[\frac{7429}{17 \cdot 19}=?\]
TinaSh
  • TinaSh
So far I have done , 17/7429 = 437 /23 = 19
TinaSh
  • TinaSh
that leaves me with 1 , if i divide it within 19 itself
freckles
  • freckles
is this what you meant to say: \[\frac{7429}{17 \cdot 19}=\frac{7429}{323}=23\]
freckles
  • freckles
which means 17*19*23=7429
TinaSh
  • TinaSh
kinda
freckles
  • freckles
oh I think I get what you are saying but those fractions aren't equal
freckles
  • freckles
\[\frac{7429}{17}=437 \\ \frac{437}{23}=19\]
freckles
  • freckles
first fraction gives 7429=17(437) then second fraction says 437=23(19)
freckles
  • freckles
so replace 437 in 7429=17(437) with 23(19) so 7429=17(23*19)
freckles
  • freckles
and you did it girl good job!
TinaSh
  • TinaSh
Oh my gosh thank you so much <3
freckles
  • freckles
and 17,19,23 are all prime because they are only divisible by themselves or 1
TinaSh
  • TinaSh
Can I get this straight first XD I wanna be completely sure 17/7421 = 19 divide by 23 or what? Oh my gosh I am confusing myself

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