three birthdays

[milagros317]

Alice, a grandmother, was celebrating her mutual birthday with her daughter, Barbara, and her granddaughter, Cindy. All three women have the same birthday.

"Gee, Mom," said Barbara, "today you are just as far over 70 as I am under 70."

"Yes, dear," said Alice, "and that is just a silly way of saying that the sum of our ages is 140. Do you realize that today I am triple the age that you were back when I was your current age?"

"Certainly," said Barbara after a quick mental calculation. "And today I am quadruple the age that my daughter Cindy was back when I was her current age."

How old are the three of them?

 

[rdhd]

No bites? I tried, but guess my thinking abilities have deteriorated with age. Seems to be simple, but obviously isn't. Will you eventually post the solution? (I'm still beating my brain with it)

 

[Blakaddre]

35, 56, and 84. Took way longer than it needed to, but I got there.

 

[Tenebrae]

I suck at Math, so bear with me here 😛 I do like logic riddles such as this one, though, so I can't help giving this a shot:

I'd say, Alice is 84, Barbara is 56, and... I can't figure out a logical way to calculate Cindy's age at the moment 😀

When Alice was 56, Barbara was 28 (28*3=84)

When Barbara was Cindy's current age, Cindy was 14 (14*4=56)

 

[rdhd]

Tenebrae, think you got it. The math works. I catch on now.......

 

[milagros317]

35, 56, and 84. Took way longer than it needed to, but I got there.

These are correct!

 

[milagros317]

I suck at Math, so bear with me here 😛 I do like logic riddles such as this one, though, so I can't help giving this a shot:

I'd say, Alice is 84, Barbara is 56, and... I can't figure out a logical way to calculate Cindy's age at the moment 😀

When Alice was 56, Barbara was 28 (28*3=84)

When Barbara was Cindy's current age, Cindy was 14 (14*4=56)

This is correct!

To get Cindy's current age, continue by noting that 56-x = 14+x (where x is the number of years ago that Barbara was Cindy's current age).
Then x=21, so 56-x=14+x=35, Cindy's current age.

 

[Tenebrae]

This is correct!

To get Cindy's current age, continue by noting that 56-x = 14+x (where x is the number of years ago that Barbara was Cindy's current age).
Then x=21, so 56-x=14+x=35, Cindy's current age.

Ahhhh of course! Thank you so much for this 🙂

I wish I had a math teacher as nice as you when I was a kid. Maybe I would have fared better (and my parents would have been grateful 😀) 😉

 

[rdhd]

Just curious. Other than outright guessing, is there a way to get either Alice's or Barbara's age? Which then leads into Cindy's age. Guess I was trying to be too analytic.

 

[BlasterMaster]

I refuse your attempt to make my brain do math. 😛

 

[milagros317]

Just curious. Other than outright guessing, is there a way to get either Alice's or Barbara's age? Which then leads into Cindy's age. Guess I was trying to be too analytic.

It can be solved using high school algebra:

Let a, b, and c represent the ages of Alice, Barbara, and Cindy, respectively.
Let z represent the number of years since Alice was Barbara's age.

We know that a+b = 140
and that a = 3*(b-z) = 3b-3z
and also that a-z = b

Use your favorite method for solving 3 linear equations in 3 unknowns to achieve a=84, b=56, z=28.
Then solve for c as in post number 7 in this thread, above.

 

[milagros317]

I refuse your attempt to make my brain do math. 😛

Once you're done with schools/colleges, nobody can force you to do math. Some people (obviously including me) find it to be fun. 😀