Solving the Puzzle: Ann and Mary's Ages

[bamboozle]

Can anyone solve this puzzle that a friend sent to me?

When Ann is half as old as Mary will be when Mary is three times as old as Mary is now. Mary will be five times as old as Ann is now. Neither Ann nor Mary may vote. How old is Ann?

 

[matt grime]

let the ages be A and M in hte obvious fashion, and suppose that this point in the future when the ages have this property is k years away, then translatingA+k= 3M/2

(at this point when anne is k years older, he age is 3/2 of mary's current age)

simultaneously,

M+k=5A

mary is 5 times as old as anne is.

comparing and eliminating the k,

5M=12A

we're presuming that M and A rea integers less than 18. So as 12 is prime to 5, it muust be that M is a multiple of 12, and the only one that assures minority is M=12, and hence A=5.

 

[M98Ranger]

This puzzle is a classic example of a mathematical problem that requires careful reading and logical thinking to solve. It may seem confusing at first, but with a bit of patience and focus, anyone can solve it.

To start, let's break down the information given in the puzzle. We know that Ann is currently younger than Mary, as neither of them can vote yet. We also know that at some point in the future, Mary will be three times as old as she is now, and Ann will be half as old as Mary will be at that time. Additionally, we are told that at this future point, Mary will be five times as old as Ann is now.

Now, let's assign variables to represent Ann and Mary's current ages. Let's say Ann's age is represented by the letter "a" and Mary's age is represented by the letter "m". Using this information, we can create equations to represent the relationships between their ages.

First, we know that at some point in the future, Mary will be three times as old as she is now. This can be represented by the equation m = 3m. We also know that at this same point, Ann will be half as old as Mary will be. This can be represented by the equation a = 1/2 (3m). Simplifying this equation, we get a = 3/2m.

Next, we are told that at this future point, Mary will be five times as old as Ann is now. This can be represented by the equation m = 5a. Now, we can substitute the value of a from our previous equation into this one. This gives us m = 5(3/2m), or m = 15/2m.

To solve for m, we can multiply both sides of the equation by 2, giving us 2m = 15m. Then, we can subtract 2m from both sides, leaving us with 0 = 13m. This means that m must equal 0, which is impossible since neither Ann nor Mary can be younger than 18.

This tells us that our initial assumption was incorrect and that Ann must be older than Mary. Let's try assigning different values to their ages and see if we can find a solution that fits all the given information.

Let's say Ann is 20 and Mary is 24. This fits the criteria that neither of them can vote yet. Plugging these values