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Insane Math


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Wow. I needed a spreadsheet to figure this one out.

I got

Your age = 33 137/319

My age = 52 182/319

I had 6 variables, 5 equations from the problem, and another logical equation. I'm double checking my answer...

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Insane Math:

My age, which plus yours is 86, is 15/16 the age you will be when I am 9/16 the age you would be if you were twice as old as I will be when I am twice your age. How old am I and how old are you?

How to Solve: Untangle the problem...

1. One day I will be 2x and you will be x

|----------|-----|

.......me(2x)....you(x)

So I am always older than you by x years

2. When you are twice 2x, I am 5x, so when you are 4x I am 5x (duh, cuz I'm always x ahead of you). And when I am 9/16 of your 4x, I am 2.25x and you are 1.25x (again, I'm always x ahead of you).

|-----------|------|

.......me(2.25x)....you(1.25x)

3. When I am 15/16 of your 1.25x, I am 75x/64 (or x*75/64) and you are 11x/64 (or x*11/64)

I am 75 and you are 11, it adds to 86

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the age you would be if you were twice as old as I will be when I am twice your age.

My mistake was thinking "your age" was your age today, not the age you would be the year I was twice as old as you.

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Now you know how to solve these kinds of problems...

If I am twice as old as you were when I was your age, and when you are my age the sums of our ages will be 63, how old am I now and how old are you?

never saw`an answer to this one so...

27 and 18

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Insane Math:

My age, which plus yours is 86, is 15/16 the age you will be when I am 9/16 the age you would be if you were twice as old as I will be when I am twice your age. How old am I and how old are you?

that doesnt add up to 63...

The condition states: "and when you are my age the sum of our ages will be 63."

Huh? Are we reading the same puzzle? It states (bolding mine), "My age, which plus yours is 86".

Checking unreality's answer of 75 and 11 working backwards:

"when I am twice your age": In 53 years, I will be 128 and you will be 64.

"if you were twice as old as I will be when I am twice your age": If you were twice as old as 128, you'd be 256

"when I am 9/16 the age you would be": 9/16 of 256 is 144. When I'm 144, you'll be 80

"15/16 the age you will be": 15/16 of 80 is 75. I am 75.

'My age, which plus yours is 86": 86 minus 75 is 11. You are 11

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Now you know how to solve these kinds of problems...

If I am twice as old as you were when I was your age, and when you are my age the sums of our ages will be 63, how old am I now and how old are you?

After unreality answered the original problem he(she) (sorry i don't know him/her) wrote this problem!

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Now you know how to solve these kinds of problems...

If I am twice as old as you were when I was your age, and when you are my age the sums of our ages will be 63, how old am I now and how old are you?

After unreality answered the original problem he(she) (sorry i don't know him/her) wrote this problem!

Ahh, I see. I'll take a look at that one now.

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If I am twice as old as you were when I was your age, and when you are my age the sums of our ages will be 63, how old am I now and how old are you?

You are 28 and I'm 21.

your answer doesn't fit the first condition. it does fit the second tho.

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your answer doesn't fit the first condition. it does fit the second tho.

Sure it does.

"If I am twice as old as you were when I was your age"

When the speaker was 21, I was 14. He is now 28, which is twice 14.

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nope i saw it in a book... i hardly even get the answer mate ;D

yeah, and you've helped me waste 2 hours of my life (paid time b/c i'm at work!).

i'm making some kind of mistake on your second problem. maybe you can point it out for me.

i am 2x and you are x (i'm pretending i'm the one proposing the question. sorry for the confusion).

when you are my age, 2x, i will be 3x (because i'm x years older than you)

our combined age, 5x, equals 63 years

x equals 12.6

2x equals 25.2, your age. 3x equals 37.8, my age. 25.2 plus 37.8 equals 63.

i guess i was expecting nice round numbers. did i get this wrong? where's my mistake?

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Sure it does.

"If I am twice as old as you were when I was your age"

When the speaker was 21, I was 14. He is now 28, which is twice 14.

oops. i guess that's it. i was thinking "if i am twice as old as you are when I was your age."

i like math problems, but i hate written problems that make you think, and think, umm and think...

can you post a description of how you analyzed and solved that problem...so i don't have to hurt my brain trying to turn it into equations. please. =)

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can you post a description of how you analyzed and solved that problem...so i don't have to hurt my brain trying to turn it into equations. please. =)

I realize the last post to this thread is pretty old, but I've been dying to unload my solution so here goes.

Let x1 = My age now

Let y1 = Your age now

Let x2 = My age when you are my age

Let y2 = Your age when you are my age (in otherwords, my age now -- x1).

unreality's original problem: "If I am twice as old as you were when I was your age, and when you are my age the sums of our ages will be 63, how old am I now and how old are you?"

Work backwords.

We know that "... when you are my age the sums of our ages will be 63."

Thus, x2 + y2 = 63

Now solve for x2: x2 = x1 + (x1 - y1) --> my age now + the time difference between my age and your age

We know that y2 = x1, so now we can replace the two variables in the first equation.

(x1) + (x1 + (x1 - y1)) = 63

Simplify: 3x1 - y1 = 63

Now that that is set up, move onto the first part of the problem: "...I am twice as old as you were when I was your age..."

Your age when I was your age --> y1 - (x1 - y1) --> 2y1 - x1

Thus, x1 = 2(2y1 - x1) --> x1 = 4y1 - 2x1

Now solve for y1 (you can solve for either but I choose y1).

3x1 = 4y1 --> y1 = 3/4x1

Now you can replace the y1 in the first simplified equation: 3x1 - 3/4x1 = 63

You're down to one variable. Solve it out and x1 = 28. Now substitute to solve for y1.

y1 = 3/4(28) which makes y1 equal to 21.

I am 28 and you are 21.

Hope that wasn't too long and overcomplicated, and I really hope somebody is still watching this topic. Please post back if it makes sense now or needs more clarification.

Thanks,

Jeff

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