Solve Financial Equation: (2,3) & (3,1) = (1,4)

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  • Thread starter Thread starter nickoh
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Discussion Overview

The discussion revolves around solving a financial equation involving two sets of payoff scenarios represented as coordinate pairs: (2,3) and (3,1) to equal (1,4). Participants explore how to combine these pairs through addition or subtraction to achieve the target outcome, with a focus on mathematical reasoning and problem-solving techniques.

Discussion Character

  • Mathematical reasoning
  • Homework-related
  • Exploratory

Main Points Raised

  • One participant seeks assistance in determining how to combine the pairs (2,3) and (3,1) to equal (1,4), proposing an initial equation of 2x + 0.5y = (1,4) but acknowledges it may be incorrect.
  • Another participant presents a system of equations: 2x + 3y = 1 and 3x + 1y = 4, and performs algebraic manipulations to derive values for x and y, arriving at x = 1.5714 and y = -0.714.
  • A subsequent post reiterates the same calculations and expresses a preference for the fractional representation of the results as 11/7 and -5/7.
  • One participant expresses hope that their calculations are correct, indicating a lack of confidence in their mathematical skills.

Areas of Agreement / Disagreement

Participants appear to agree on the calculations presented for the values of x and y, but there is uncertainty about the correctness of the initial approach and whether the derived values truly satisfy the original problem.

Contextual Notes

The discussion does not clarify the assumptions behind the equations or the methods used to derive the values, leaving some mathematical steps unresolved.

nickoh
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Hi,

I'm hoping someone can please help me with this. I'm sure it's quite simple, but I can't get my head around it.

Essentially I need to get:

(2,3) and (3,1) to equal (1,4).

The numbers in each bracket form pay off scenarios for different securities. I need to find out how to get what amount of (2,3) and (3,1) (can be added or subtracted) will equal (1,4).

i.e. assume (2,3) is x and (3,1) is y
2x + 0.5y = (1,4)

Obviously this is incorrect, but it helps to give a picture of what I need to work out.

I'm actually stumped (I've never been good at this). Every time I try using guess and check I can get one side to work out, but not the other.

Hopefully somebody can please help me understand!
 
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Tell me, is this correct? Or am I way off?

2x + 3y = 1
3x + 1y = 4

Therefore:

3(3x + 1y = 4)
9x + 3y = 12

9x + 3y =12
-
2x + 3y = 1

7x + 0y = 11

x = 1.5714
y = -0.714
 
nickoh said:
Tell me, is this correct? Or am I way off?

2x + 3y = 1
3x + 1y = 4

Therefore:

3(3x + 1y = 4)
9x + 3y = 12

9x + 3y =12
-
2x + 3y = 1

7x + 0y = 11

x = 1.5714
y = -0.714

Those are the numbers I got too. I prefer 11/7 and -5/7 though.
 
Thanks M R,

I'm hoping we are both correct, it seems logical. I've clearly forgotten a lot of maths since my high school days!
 

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