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    Would someone give me steps to solve it without telling me the answer, I know it's simple algebra but I want to learn the quickest way.

    Fernando chooses 3 different whole numbers between 1 and 40
    The first number is a square number
    The second number is 4 multiplied by the first number
    The third is a prime number and less than the first number
    The sum of all numbers is 50
    What 3 numbers has he chosen
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    (Original post by Rakkidoesscience)
    Would someone give me steps to solve it without telling me the answer, I know it's simple algebra but I want to learn the quickest way.

    Fernando chooses 3 different whole numbers between 1 and 40
    The first number is a square number
    The second number is 4 multiplied by the first number
    The third is a prime number and less than the first number
    The sum of all numbers is 50
    What 3 numbers has he chosen
    Call the first number x. It must be a square number.

    4 ≤ 4x ≤ 36. (Numbers need to be between 1 and 40).
    So, 1 ≤ x ≤ 9. x must be a square.

    I hope this helps.

    The rest as you've said is easy algebra, but I don't want to give away the answer!
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    (Original post by Rakkidoesscience)
    ...
    If you're stuck, writing them all out is also an option.


    First number possibilities: 1, 4, 9, 16, 25, 36

    Second number possibilities depending on the first choice: 4, 16, 36

    Third number possibilities: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31


    Then just deduce the number by trial and error by going through the numbers in the first list.

    For example;

    Let's say you choose 4 from the first list. Then the second number must be 16. Then 4+16=20 thus to make 50 you need 30 but that number is neither a prime number nor is it less than the first number.
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    Well you know the first number is 4 or 9 because all the other squares wont work when multiplied by 4(16*4>50). So i guess the fastest way is just by inspection.
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    (Original post by TheMightyBadger)
    Call the first number x. It must be a square number.

    4 ≤ 4x ≤ 36. (Numbers need to be between 1 and 40).
    So, 1 ≤ x ≤ 9. x must be a square.

    I hope this helps.

    The rest as you've said is easy algebra, but I don't want to give away the answer!
    Yep , that was the kind of algebra I was looking for I was trying to find a quicker way than trial and error
 
 
 
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