# Thread: Quadratic Simultaneous Eqns: ""J and T share money. If I square J's money and add..."

1. ## Quadratic Simultaneous Eqns: ""J and T share money. If I square J's money and add..."

Hi all

Can someone give me a hint on how to solve the below please?

"Jim and Tim are sharing money. If I square Jim's money and add on Tim's, I get £10,050. If I square Tim's money and add on Jim's, I get £2,600. How much money does each have?"

Regards

Jim

2. Originally Posted by Jim77
Can someone give me a hint on how to solve the below please?

"Jim and Tim are sharing money. If I square Jim's money and add on Tim's, I get £10,050. If I square Tim's money and add on Jim's, I get £2,600. How much money does each have?"
A good place to start would probably be with picking variables to stand for the unknowns. What variables did you pick, and how did you define them?

Thank you!

3. j^2 + t = 10,050
t^2 + j = 2,600

4. Originally Posted by Jim77
j^2 + t = 10,050
t^2 + j = 2,600
Okay; you've jumped ahead to equations. These equations contain the variables "j" and "t". From the way you've used the variables, I believe you defined them as follows:

. . .variables:
. . . . .Tim's money: t
. . . . .Jim's money: j

If this is correct, then your equations look to be accurate reflections of the relationships given in the exercise.

So now you have two equations in two unknowns. What method(s) have you been taught for solving systems of non-linear equations? For instance, are you familiar with "substitution"? If you are, how might that tool be applied to this system? Where does this lead?

5. Rearrange the second equation to give:

j = 2600 - T^2

Is this correct?

6. anyone?

7. Originally Posted by Jim77
Rearrange the second equation to give:

j = 2600 - T^2

Is this correct?
Yes, this is correct.

This allows you to restate the other equation how?

By the way, most of the volunteers here, who are paid not a penny, live in North America, which is at least 5 hours behind time in the UK and may be 10 hours behind. Unpaid volunteers are not necessarily going to leap from bed on a Sunday morning to work on math problems.

8. Originally Posted by Jim77
j^2 + t = 10,050
t^2 + j = 2,600
I didn't get far using substitution. Try subtracting the second equation from the first.

9. Originally Posted by Jonathan
I didn't get far using substitution. Try subtracting the second equation from the first.
Sorry could you expand on that a little bit please?

10. Originally Posted by Jim77
Sorry could you expand on that a little bit please?
The admins of this site are not happy if a full solution is given early, so I can only give hints.
In his reply Subhotosh Khan is assuming that this question is an exercise in using substitution and wants you to explain what you have learnt so far.
I believe that that there is a neater solution.

(1) j^2 + t = 10,050
(2) t^2 + j = 2,600
Make a new equation by subtracting terms of (1) from those of (2)
j^2 + t - t^2 - j = 10,050 - 2,600
see whether you can anything of this

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