# Thread: Is it possible ?

1. ## Is it possible ?

I have an equation in form of (a+b)*c =d, where "a" and "c" are unknown quantities.
Example, assigning b=4 and d=188, the equation now becomes:
(a+4)*c=188

1) Is it possible to derive the value of "a" by any means ?
2) What is the contribution of 4 in the answer 188 in relation with "a"
3) Does this gives rise to probability values for "a". If yes, is there any constant for this probability ?

mahesh

2. Hi,

1. What do you mean by "derive" ? Do you mean finding $\displaystyle a$ in function of the other variables ? Here, it is possible, because :

$\displaystyle (a + 4) \times c = 188$

$\displaystyle a + 4 = \frac{188}{c}$

$\displaystyle a = \frac{188}{c} - 4$, and therefore by extension it becomes $\displaystyle a = \frac{d}{c} - b$

$\displaystyle (a + 4) \times c = 188$

$\displaystyle a + 4 = \frac{188}{c}$

$\displaystyle 4 = \frac{188}{c} - a$, and therefore by extension it becomes $\displaystyle b = \frac{d}{c} - a$

3. It could give rise to probability values, you could try to study this :

$\displaystyle a = \frac{d}{c} - b$

It is equivalent to your first equation, except $\displaystyle a$ is the subject, maybe you could investigate what happens to $\displaystyle a$ when you change $\displaystyle b$, $\displaystyle c$ or $\displaystyle d$. But I believe you will not reach a concrete result easily .

3. Thanks Bacterius.

"But I believe you will not reach a concrete result easily"

Yes, I know, it will be not easy to find a concrete answer to such equations.
Actually, I want to find out specific constant for numbers ending with 4. e.g., 4,14,24,34....

Example.
(a+b)*c =d

1) The value of "a" is in multiples of 10. (10,20,30...)
2) "b" is always 4. i.e, (a+b) can be 14,24,34...

Because the equation has two unknown quantities a and c, there is no definite value for "a"

I wonder, if using the contribution of "b=4" in the answer "d=188", somehow leads to find the value of "a" by some definite means !

4. Perhaps you could use modular arithmetic tools (mod 10) in order to express all possible $\displaystyle a$'s in a formula manner (eg all $\displaystyle a$ have the form [expression]). But this is outside the scope of pre-algebra and algebra.

5. Using modular arithmetic method involves recursive calculation which is CPU expensive. So I ruled it out in the first place before posting to forums in a hope that someone has researched such problems.

Well, I will try to find if some "probability constant for specific numbers" can be discovered, and post my findings here.

Please let me know if you come across concrete solution for such equations where some value(a) is an integral part of an answer along with another unknown quantity(c).

Thanks.