what am I doing wrong here?

I hope my post is not too cryptic. If so, please let me know. I know the correct answer to this problem...it i s given in the back of the book. the old man is 63.
 
I think you are solving the quadratic incorrectly and it is the wrong quadratic?
So if grandpa's age is T3 we have T^2 = 3x10 +T ( the square of the tens digit is the same as the age reversed)

when you have T^2 = 30+T
rearrange as T^2-T-30=0

What methods do you have to solve quadratics? Factorising ring any bells?
 
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Honestly, I think using a quadratic at all is a bit overkill for this problem. The answer practically falls directly into place if you think about it for just a bit, rather than treat as a "math" problem. We want to find an age, so it's most likely going to be either a two-digit or a three-digit number. Thus, the age reversed will be (three hundred and something) or (thirty something). We're also told that the tens digit of the age is equal to the age reversed, so we simply need to find a one-digit number that, when squared, gives either (three hundred and something) or (thirty something).

This is where the aforementioned "just think about it a bit" strategy comes into play. The largest one-digit number is 9, and 92 = 81, so we know for sure that Grandpa Drac's age has two digits. Going one step further, it should be immediately obvious why the tens digit must be 6, since 62 = 36, but 52 = 25 and 72 = 49. Then we put these pieces of information together, et voila, Grandpa Drac is 63 years old. No solving a quadratic required.

Edit: Somehow I missed the "square" part that was suppose to be attached to 72. Sorry about that.
 
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When playing around with a number and that number reversed,
remember that the difference is always divisible by 9.
Example: 4321 - 1234 = 3087 = 343*9
 
allegansveritatem said:
At far left is my solution …
Click to expand...
I don't see your solution; it looks like you got stuck, after dividing each side by T.

I agree with apple2357. The first step in solving T^2=30+T is to put the quadratic equation into standard form:

ax^2 + bx + c = 0

This way, you can see the values of the coefficients a,b,c (for use in the Quadratic Formula), and it also gives you a trinomial (to try factoring, instead).

T^2 - T - 30 = 0

We know this polynomial factors nicely because its Discriminant (b^2-4ac) is a perfect square (121). :cool:
 
ksdhart2 said:
Honestly, I think using a quadratic at all is a bit overkill for this problem.
Click to expand...
I don't know the context of the exercise, but I agree this one can be reasoned out mentally. On the other hand, I don't find issue with taking an algebraic approach. I've seen scenarios that don't require a quadratic model assigned as practice for writing/solving quadratic equations.

Heck -- even if the context is a brainteaser, I would probably still use algebra because I'm lazy (overall). :cool:
 
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mmm4444bot said:
I don't know the context of the exercise, but I agree this one can be reasoned out mentally. On the other hand, I don't find issue with taking an algebraic approach. I've seen scenarios that don't require a quadratic model assigned as practice for writing/solving quadratic equations.

Heck -- even if the context is a brainteaser, I would probably still use algebra because I'm lazy (overall). :cool:
Click to expand...

I only used algebra because the OP did and was trying to help their reasoning rather than just ignore what they did and say here you go...
 
apple2357 said:
I think you are solving the quadratic incorrectly and it is the wrong quadratic?
So if grandpa's age is T3 we have T^2 = 3x10 +T ( the square of the tens digit is the same as the age reversed)

when you have T^2 = 30+T
rearrange as T^2-T-30=0

What methods do you have to solve quadratics? Factorising ring any bells?
Click to expand...

I didn't think to try the quadratic formulation. I guess I should have the moment a square entered the picture.
 
ksdhart2 said:
Honestly, I think using a quadratic at all is a bit overkill for this problem. The answer practically falls directly into place if you think about it for just a bit, rather than treat as a "math" problem. We want to find an age, so it's most likely going to be either a two-digit or a three-digit number. Thus, the age reversed will be (three hundred and something) or (thirty something). We're also told that the tens digit of the age is equal to the age reversed, so we simply need to find a one-digit number that, when squared, gives either (three hundred and something) or (thirty something).

This is where the aforementioned "just think about it a bit" strategy comes into play. The largest one-digit number is 9, and 92 = 81, so we know for sure that Grandpa Drac's age has two digits. Going one step further, it should be immediately obvious why the tens digit must be 6, since 62 = 36, but 52 = 25 and 72 = 49. Then we put these pieces of information together, et voila, Grandpa Drac is 63 years old. No solving a quadratic required.

Edit: Somehow I missed the "square" part that was suppose to be attached to 72. Sorry about that.
Click to expand...

I really don't get you at all. Why does it follow that if the age is going to be a two or three digit number that it is going to be either three hundred something or thirty something?
 
Denis said:
When playing around with a number and that number reversed,
remember that the difference is always divisible by 9.
Example: 4321 - 1234 = 3087 = 343*9
Click to expand...

That is one of the ten thousand (a rhetorical expression meaning (infinitely many) things that I don't know--until today that is. Very interesting.
 
mmm4444bot said:
I don't see your solution; it looks like you got stuck, after dividing each side by T.

I agree with apple2357. The first step in solving T^2=30+T is to put the quadratic equation into standard form:

ax^2 + bx + c = 0

This way, you can see the values of the coefficients a,b,c (for use in the Quadratic Formula), and it also gives you a trinomial (to try factoring, instead).

T^2 - T - 30 = 0

We know this polynomial factors nicely because its Discriminant (b^2-4ac) is a perfect square (121). :cool:
Click to expand...

Yes, I got stuck. I will try the quadratic and the factoring of same.
 
mmm4444bot said:
I don't know the context of the exercise, but I agree this one can be reasoned out mentally. On the other hand, I don't find issue with taking an algebraic approach. I've seen scenarios that don't require a quadratic model assigned as practice for writing/solving quadratic equations.

Heck -- even if the context is a brainteaser, I would probably still use algebra because I'm lazy (overall). :cool:
Click to expand...

It is a problem from an algebra book, therefore I want to approach it as the author intended it be approached. I want to know how to do it algebraically. Also, I am really not getting the reasoning of those who are using "pure reason" here.
 
allegansveritatem said:
It is a problem from an algebra book, therefore I want to approach it as the author intended it be approached. I want to know how to do it algebraically.
Click to expand...
Well, good, now you have a quadratic equation to solve algebraically (using any method you've seen that makes sense). :cool:

Thank you, for continuing to show your work, if you have more questions about this exercise.
 
allegansveritatem said:
I didn't think to try the quadratic formulation. I guess I should have, the moment a square entered the picture.
Click to expand...
But you did formulate a quadratic relationship! :D

Your work shows it: T^2 = 30 + T

Or, did you intend to say, "I didn't think to put my quadratic equation in standard form." That's the step you needed to recognize, instead of dividing by T.
 
allegansveritatem said:
I really don't get you at all. Why does it follow that if the age is going to be a two or three digit number that it is going to be either three hundred something or thirty something?
Click to expand...

The age itself won't necessarily be (three hundred and something) or (thirty something), but the age reversed will be. One of the pieces of information we're given is that the units digit of Grandpa Drac's age is 3. "Units digit" is another way of saying "ones digit" so we know the age must end in 3. From this, we can easily see that the age reversed must start with 3.
 
Wellllll...one thing fer sure:
playing around with age ain't the best way to "introduce" the quadratic equation!
 
Denis said:
… playing around with age ain't the best way to "introduce" the quadratic equation!
Click to expand...
Playing around isn't the best way to introduce anything!

It's a fun way to discover stuff, though. :cool:
 
allegansveritatem said:
I really don't get you at all. Why does it follow that if the age is going to be a two or three digit number that it is going to be either three hundred something or thirty something?
Click to expand...
If you reversed his age it would be in the 3 hundred range or in the 30 range since the unit digit is 3 (if you reverse 143 you get 341 (It is in the 3 hundred range) and if you reverse 73 you get 37 (which is in the 30's).
Now when you square the tens digit you get his age in reverse. So if the tens digit is 9, then his age 18 (since 9^2 =81). but this can't be since the unit digit must be 3 not 1. 8^2 =64 so the reverse will be 46 which does not end in a 3. 7^2 =49 so the reverse will be 94 which does not end in a 3. But 6^2 =36 so the reverse will be 63 which does end in a 3. No other value for the tens place starts with a 3, so grandpa's age is 63.
 
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