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Algebra

Anna's age is twice that of David's and half that of Bob's. The total of all their ages is 21. How old is Bob?


Comments

  1. First we need to set the variables:

    Let Anne be 'a'. Let Bob be 'b'. Let David be 'd'.

    Now we can create a formula:
    a + b + d = 21.

    Next we need to substitute the variables for one after calculating it. This may sound confusing but it will make sense:

    a = 2d This is because the question states that Anne's age is twice that of David's.
    b = 2a This is because the question also states Anna's age is half that of Bob's.
    This then means that b = 4d when you substitute the a from the first equation into the second.

    Now, remember that formula we created earlier? We can use that now by substituting the values that we've calculated:

    2d + 4d + d = 21
    7d = 21
    d = 3
    Now it may seem like we're done, but remember, the question asks for Bob's age. This means we substitute 4 * d into our new value of d and we get 4 * 3, which is 12. NOW, we're done

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