Alberta's Age
Alberta won't reveal her age. Can you work it out from these clues?
Age
14 to 16
Challenge level
Problem
The two digits of Alberta's age are interchanged, and then 1 is added to the result.
The answer is half of Alberta's present age.
How old is Alberta?
Student Solutions
Answer: 52
Clare's method
Interchanging the digits should make the number smaller (about half), so the first digit should be greater (about double), like 42, 84 (only such pairs since Alberta's age should be even).
42, 24 +1 is a bit too big so try making 42 a bit bigger
52, 25 +1 = 26, perfect!
84, 48 +1 = 49 is half of 98, much too big
94, 49 +1 = 50 no
Charlie's method
If Alberta is $ab$ years old, then her age is $10a+b$
If the digits are interchanged this becomes $ba$, so $10b+a+1$ is half of $10a+b$ $$\begin{align}\therefore 10a+b &=2(10b+a+1)\\
10a+b&=20b+2a+2\\
8a&=19b+2\end{align}$$
| $b$ | $19b+2$ | $a$ |
|---|---|---|
| 1 | 21 | Not a whole number |
| 2 | 40 | 5 |
| 3 | 59 | Not a whole number |
| 4 | 78 | Not a whole number |
| 5 | 97 | Greater than 10 |
$\therefore a=5, b=2$, Alberta is $52$