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TinaSh

  • one year ago

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?

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  1. freckles
    • one year ago
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    so we have \[a \cdot b \cdot c=7429\]

  2. freckles
    • one year ago
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    we know prime numbers are odd for the most part

  3. freckles
    • one year ago
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    and we know 7429 is not even so none of the primes are 2

  4. freckles
    • one year ago
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    two of her children are teenagers so they could be 13,17, or 19

  5. freckles
    • one year ago
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    I would probably try to write the prime factorization of 7429

  6. freckles
    • one year ago
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    can you do that?

  7. TinaSh
    • one year ago
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    wait what are prime numbers? :$

  8. freckles
    • one year ago
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    prime numbers are integers that are only divisible by themselves and 1.

  9. freckles
    • one year ago
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    the key here is just to write 7429 in prime factorization that is all there is to the problem

  10. freckles
    • one year ago
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    like for example 25=5*5 or 5^2 31 is prime 25 was not umm... 2 is the only even prime

  11. TinaSh
    • one year ago
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    I dont even know what factorization means >.< I missed few days of school.

  12. campbell_st
    • one year ago
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    one tip... given the last digit is 9... I'd divide the original number by 17

  13. freckles
    • one year ago
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    example: the prime factorization of 12=2*2*3

  14. TinaSh
    • one year ago
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    thanks <3

  15. campbell_st
    • one year ago
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    then see if the other 2 primes in the teens divides evenly

  16. TinaSh
    • one year ago
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    I don't know , I will try to figure it out thanks though

  17. freckles
    • one year ago
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    well the key to help was the teenager part

  18. TinaSh
    • one year ago
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    yeah , teens

  19. freckles
    • one year ago
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    "so they could be 13,17, or 19" exactly two of these numbers will be factors

  20. freckles
    • one year ago
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    then you have to find the other factor by divide 7429 by the product of two teenagers

  21. freckles
    • one year ago
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    what is 7429 divided by 13 ?

  22. TinaSh
    • one year ago
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    2476.3

  23. freckles
    • one year ago
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    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

  24. freckles
    • one year ago
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    so you only have to find one last factor

  25. freckles
    • one year ago
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    \[\frac{7429}{17 \cdot 19}=?\]

  26. TinaSh
    • one year ago
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    So far I have done , 17/7429 = 437 /23 = 19

  27. TinaSh
    • one year ago
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    that leaves me with 1 , if i divide it within 19 itself

  28. freckles
    • one year ago
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    is this what you meant to say: \[\frac{7429}{17 \cdot 19}=\frac{7429}{323}=23\]

  29. freckles
    • one year ago
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    which means 17*19*23=7429

  30. TinaSh
    • one year ago
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    kinda

  31. freckles
    • one year ago
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    oh I think I get what you are saying but those fractions aren't equal

  32. freckles
    • one year ago
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    \[\frac{7429}{17}=437 \\ \frac{437}{23}=19\]

  33. freckles
    • one year ago
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    first fraction gives 7429=17(437) then second fraction says 437=23(19)

  34. freckles
    • one year ago
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    so replace 437 in 7429=17(437) with 23(19) so 7429=17(23*19)

  35. freckles
    • one year ago
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    and you did it girl good job!

  36. TinaSh
    • one year ago
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    Oh my gosh thank you so much <3

  37. freckles
    • one year ago
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    and 17,19,23 are all prime because they are only divisible by themselves or 1

  38. TinaSh
    • one year ago
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    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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