1. ## equation with integers

Find the whole numbers for A and B that satisfy the following equation.

A+B = A.B A and B cannot be zero.
2

AND

Every once in a while a calendar year will be a palindrome, which means it reads the same forward and backward. Starting with 10 a.d. , can you come up with a pair of palindrome years that are...

A) 110 Years apart?
B) 11 Years apart?
C) 10 years apart?
D) 2 Years apart?

Thanks SOOOOOO much!

2. Originally Posted by annie3993
Find the whole numbers for A and B that satisfy the following equation.

A+B = A.B A and B cannot be zero.
2

AND

Every once in a while a calendar year will be a palindrome, which means it reads the same forward and backward. Starting with 10 a.d. , can you come up with a pair of palindrome years that are...

A) 110 Years apart?
B) 11 Years apart?
C) 10 years apart?
D) 2 Years apart?

Thanks SOOOOOO much!
You have 2 unknowns - A and B, so you need simultaneous equations to find both. 1 equation is not enough.

3. Originally Posted by annie3993
Find the whole numbers for A and B that satisfy the following equation.

A+B = A.B A and B cannot be zero.
2
Note that A.B can be written as $\displaystyle A+\frac{B}{10}$

so now we get

$\displaystyle \frac{A+B}{2}=A+\frac{B}{10}$ multiply by 10 to clear the fractions

$\displaystyle 5A+5B=10A+B \iff -5A=-4B \iff A=\frac{4}{5}B$

Since A need to be a whole number B needs to be a multiple of the denominator 5

$\displaystyle b=5, A=\frac{4}{5}(5)=4$

A=4 and B=5.

I hope this helps.

4. i still can't get this one...

Every once in a while a calendar year will be a palindrome, which means it reads the same forward and backward. Starting with 10 a.d. , can you come up with a pair of palindrome years that are...

A) 110 Years apart?
B) 11 Years apart?
C) 10 years apart?
D) 2 Years apart?

Thanks SOOOOOO much!

5. Originally Posted by annie3993
i still can't get this one...

Every once in a while a calendar year will be a palindrome, which means it reads the same forward and backward. Starting with 10 a.d. , can you come up with a pair of palindrome years that are...

A) 110 Years apart?
B) 11 Years apart?
C) 10 years apart?
D) 2 Years apart?

Thanks SOOOOOO much!
If there is an algorithm to determin this I do not know it.

You just have to guess(make educated guesses) and check

for exapmle for D)

1001 is a one and two less than it is 999.

Write some out and see what you can get

6. ## Thanx

Alright, i'll try that. Thanx 4 your help!

7. How does A.B = A + B/10?

:S

A.B = A*B, no?

I don't get this.

8. i don't really get it either, but i desperately need extra credit, so i'll take any answer...

9. Originally Posted by sean.1986
How does A.B = A + B/10?

:S

A.B = A*B, no?

I don't get this.

A and B are digits the peroid doesn't represent multiplication.

The period is a decimal point so what the question is asking is

$\displaystyle \frac{4+5}{2}=4.5$

$\displaystyle \frac{9}{2}=4.5$

$\displaystyle 4.5=4.5$

I hope this clears it up.

10. Yes it does, haha. I thought it was multiply.

11. A) 1221 1331
B) 22 11
C) 121 131
D) 1001 999

12. Originally Posted by TheEmptySet
A and B are digits the peroid doesn't represent multiplication.

The period is a decimal point so what the question is asking is

$\displaystyle \frac{4+5}{2}=4.5$

$\displaystyle \frac{9}{2}=4.5$

$\displaystyle 4.5=4.5$

I hope this clears it up.
For extra credit problems we should only be giving hints and commenting on solutions proposed by the original poster.

Giving them a full answer that can be handed in is helping no one, whatever the original poster thinks.

RonL