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how old am I
- Thread starter bekah24h
- Start date
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bekah24h said:How old am I? My age is a perfect square number of years greater than a perfect square number; it is also a perfect square number of years less than a perfect square. Next year, my age will be a prime number less than 50
Next year, my age will be a prime number less than 50
Does the sentence above mean:
Next year, my age will be a prime number - less than 50
Next year, my age will be - a prime number less than 50
In either case:
Start defining your variable:
Let my age = A
Now continue.....
Please show us your work/thoughts, indicating exactly where you are stuck - so that we may know where to begin to help you.
Hello, bekah24h!
There is no formula for this type of problem.
. . We must resort to intelligent guesswork.
Let \(\displaystyle A\) = my age.
\(\displaystyle \text{Then: }\;\begin{array}{ccccc}A\text{ is the sum of two squares:} & A &=& a^2+b^2 \\ A\text{ is the difference of two squares:} & A &=& c^2-d^2 \end{array}\)
Consider the square numbers:
. . \(\displaystyle \begin{array}{ccccccccccccccc}1 & \boxed{4} & 9 & 16 & 25 & \boxed{36} & 49 & 64 & \boxed{81} & 100 & \boxed{121} & 144 & 169 & \hdots\)
. . . .. \(\displaystyle \underbrace{\qquad\qquad\qquad\qquad\quad}_{\text{sum of 40}} \qquad\qquad\quad \underbrace{\qquad\qquad\qquad\quad}_{\text{difference of 40}}\)
Therefore, my age is 40.
How old am I?
My age is a perfect square number of years greater than a perfect square number.
It is also a perfect square number of years less than a perfect square.
Next year, my age will be a prime number less than 50.
There is no formula for this type of problem.
. . We must resort to intelligent guesswork.
Let \(\displaystyle A\) = my age.
\(\displaystyle \text{Then: }\;\begin{array}{ccccc}A\text{ is the sum of two squares:} & A &=& a^2+b^2 \\ A\text{ is the difference of two squares:} & A &=& c^2-d^2 \end{array}\)
Consider the square numbers:
. . \(\displaystyle \begin{array}{ccccccccccccccc}1 & \boxed{4} & 9 & 16 & 25 & \boxed{36} & 49 & 64 & \boxed{81} & 100 & \boxed{121} & 144 & 169 & \hdots\)
. . . .. \(\displaystyle \underbrace{\qquad\qquad\qquad\qquad\quad}_{\text{sum of 40}} \qquad\qquad\quad \underbrace{\qquad\qquad\qquad\quad}_{\text{difference of 40}}\)
Therefore, my age is 40.