### Brain Teasers

# Mimi's Mathematical Moment

Fresh and invigorated after completing her algebra homework, Mimi appeared at the living room door. She held a piece of paper covered in scribbled numbers, 'm's, 'd's, and equations.

"Dad!" she announced. "Five years from now you'll be only double my age!"

"Amazing!" Dad almost looked up from the TV, but knew she hadn't finished.

"But five years ago, you were triple my age then!"

"I suppose in another ten years we'll be the same age," Dad grunted, changing channels.

How old is Mimi?

"Dad!" she announced. "Five years from now you'll be only double my age!"

"Amazing!" Dad almost looked up from the TV, but knew she hadn't finished.

"But five years ago, you were triple my age then!"

"I suppose in another ten years we'll be the same age," Dad grunted, changing channels.

How old is Mimi?

### Hint

Don't pay any attention to Dad's rather mindless comment at the end! He'd had a tough day.### Answer

Mimi is 15 (and Dad is 35).This one is probably easiest to guess and check. There are lots of little clues that help narrow down the options to guess. You might like to write some of these in the comments section.

e.g. Dad's age must have been a multiple of 6 five years ago. His age was triple Mimi's and ten years later it would be a multiple of two. So it was a multiple of both 3 and 2.

Or you could use algebra:

Let m and d represent Mimi's and Dad's ages now.

1. d-5 = 3x(m-5)

2. d+5 = 2x(m+5)

d-5 = 3m-15 ... *1*

d+5 = 2m+10 ... *2*

-10 = m-25 ... subtracting *2* from *1*

So m=15

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## Comments

Good one! I really wanted to challenge myself to do this one algebraically, but it has been a LONG time since I took algebra, so I didn't want to confuse myself with 2 variables. So I decided to only use Mimi's age as the variable, which meant I'd have to represent Dad's age as a function of Mimi's age.

The first number, chronologically anyway, is Mimi's age 5 years ago, so I went with that as my variable and called it M. Since Dad was 3 times her age 5 years ago, his age can be represented as 3M. Add 10 to that (making it ten years later) and his age would be double Mimi's new age, so it could be represented as 2 times M+10. Since Dad's age equals Dad's age, the formula I started with was 3M+10 = 2(M+10). Here's how I broke it down (after an embarrassingly long struggle to remember basic algebraic rules):

3M+10 = 2(M+10)

3M+10=2M+20

3M=2M+10

3=1/M (2M+10)

3=2+10/M

1=10/M

M=10

Since M is Mimi's age 5 years ago, add 5 to it to get her current age of 15. Whew.

The first number, chronologically anyway, is Mimi's age 5 years ago, so I went with that as my variable and called it M. Since Dad was 3 times her age 5 years ago, his age can be represented as 3M. Add 10 to that (making it ten years later) and his age would be double Mimi's new age, so it could be represented as 2 times M+10. Since Dad's age equals Dad's age, the formula I started with was 3M+10 = 2(M+10). Here's how I broke it down (after an embarrassingly long struggle to remember basic algebraic rules):

3M+10 = 2(M+10)

3M+10=2M+20

3M=2M+10

3=1/M (2M+10)

3=2+10/M

1=10/M

M=10

Since M is Mimi's age 5 years ago, add 5 to it to get her current age of 15. Whew.

Well done, JS. You did make it a bit longer than necessary, though. After line 3, you could have just subtracted 2M from both sides, to leave M=10. Glad it brought back some Algebra Skill!

Nicely done. This was a concise math problem wrapped in a well written little story. I liked this one a lot.

I like that there is a story, and not "just" a word problem.

I hated math in school and still dislike it so this was not a good teaser for me and I did not even try. Sorry!

Might be tough for some people, but right up my alley. Was very easy for me. I did great in math, but was not good in English, as somebody pointed out to me recently.

My brain hasn't done algebra in far too long!

I can't comment on whether it was easy or hard. I quickly just figured it out in my head without resorting to any equations.

I also did not get it; I was good at math when I was young but have been away from it too long.

Nice to see this one roll back around. It was fun again. I also did it in my head, but I did have to resort to the algebra. 3m - d = 10 and 2m - d = -5, subtract, m = 15.

I love math and algebra riddles, but this one was a bit too easy. A simple initial guess of 15 made sense and could be quickly proven correct.

However, I'm having trouble figuring out why Snowdog used the equations he did. Not that I'll ever see this again (well, maybe in 3 years!), but I'd love someone to explain that.

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