# Thread: Find the values of S1 & S2? Need help.

1. ## Find the values of S1 & S2? Need help.

Okay... so here's the deal

It's given

S1 + S2 = 16 ---------- Eqn. (1)

And S1 X S2 = 3(S1 + S2) = 3 X 16 = 48 -------- Eqn. (2)

The answers are S1 = 12 & S2 = 4. It says solving the eqns (1) & (2)

I don't understand how the answers can be ontained by solving (1) & (2). Exactly how can the eqns be solved??

I tried squaring both the sides in Eqn. (1). But that just brings the the square term which I need to eliminate. The way I did gave me two answers for each of S1 & S2.

However, the answers are only two, not four.

2. Originally Posted by arijit2005
Okay... so here's the deal

It's given

S1 + S2 = 16 ---------- Eqn. (1)

And S1 X S2 = 3(S1 + S2) = 3 X 16 = 48 -------- Eqn. (2)

The answers are S1 = 12 & S2 = 4. It says solving the eqns (1) & (2)

I don't understand how the answers can be ontained by solving (1) & (2). Exactly how can the eqns be solved??

I tried squaring both the sides in Eqn. (1). But that just brings the the square term which I need to eliminate. The way I did gave me two answers for each of S1 & S2.

However, the answers are only two, not four.

Solve the first equation for, say, S2:
$S_2 = 16 - S_1$

Now put that into the second equation:
$S_1 \cdot (16 - S_1) = 3(S_1 + (16 - S_1) ) = 48$

This is a quadratic equation. So expand this out and solve the quadratic. I get two sets of solutions:
$S_1 = 12,~S_2 = 4~\text{and}~S_1 = 4,~S_2 = 12$

-Dan

3. Originally Posted by topsquark
Solve the first equation for, say, S2:
$S_2 = 16 - S_1$

Now put that into the second equation:
$S_1 \cdot (16 - S_1) = 3(S_1 + (16 - S_1) ) = 48$

This is a quadratic equation. So expand this out and solve the quadratic. I get two sets of solutions:
$S_1 = 12,~S_2 = 4~\text{and}~S_1 = 4,~S_2 = 12$

-Dan

Well, yeah, this is a quadratic equation. But there's only one set of solutions [S1 = 12 & S2 = 4]. Had there been two sets of solutions, as you have already shown, shouldn't they have been mentioned in the solution book? But there's only 1 set, which is why I'm getting confused.

See, it's about the specific gravities of two substances in an alloy, where S1 & S2 represent the sp. gravities of the 1st & 2nd substances respectively. Now one substance can't have to sp. gravities, can it?

Is there any other way you can get only one set of solutions?

4. Without knowing more about the problem, you can't rule out one of the possibilities. Do you know what the two substances in the alloy are?

5. Originally Posted by arijit2005
But there's only one set of solutions [S1 = 12 & S2 = 4]. Had there been two sets of solutions, as you have already shown, shouldn't they have been mentioned in the solution book? But there's only 1 set, which is why I'm getting confused.
IF one set only, then problem MUST state: where S1 > S2

6. No.. I'm not told what the substances are....

7. Originally Posted by Wilmer
IF one set only, then problem MUST state: where S1 > S2
Well, that condition is not given either...

Anyways..

Thank you all for taking the time to respond..

8. Originally Posted by arijit2005
But there's only one set of solutions [S1 = 12 & S2 = 4]. Had there been two sets of solutions, as you have already shown, shouldn't they have been mentioned in the solution book? But there's only 1 set,.....
REPEATING: IF there's only ONE set of solutions in "the book",
then "the book" SHOULD specify S1 > S2.
If x and y are positive integers > 0 and x + y = 3, then if there is ONLY one solution,
x > y or y > x MUST be specified