Farhan and Junhao score points

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Discussion Overview

The discussion revolves around a problem involving two players, Farhan and Junhao, who initially had the same number of points in a game. After gaining additional points, the relationship between their scores changes, leading to a question about their original scores. The scope includes mathematical reasoning and problem-solving related to algebraic expressions and equations.

Discussion Character

  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant proposes letting \(F\) and \(J\) represent the points of Farhan and Junhao, respectively, and notes that after gaining points, Farhan has three times the points of Junhao.
  • Another participant suggests using a single variable \(O\) for the original points both players had, leading to the equation \(O + 470 = 3(O + 50)\) to solve for \(O\).
  • There is a correction regarding the use of variables, emphasizing that the same letter should not represent different values at different times, which leads to confusion in the equations presented.
  • One participant calculates \(O\) to be 160, while another expresses uncertainty about their calculations and arrives at a negative value for \(J\).
  • Participants discuss the algebraic manipulation of the equations, with some clarifying the correct relationships and expressions needed to solve the problem.

Areas of Agreement / Disagreement

Participants express differing views on the correct approach to the problem, with some arriving at a solution while others remain uncertain or confused about their calculations. There is no consensus on the correct method or final answer, as some participants correct each other without resolving the overall disagreement.

Contextual Notes

There are limitations in the clarity of variable definitions and the algebraic steps taken, leading to confusion in the problem-solving process. The discussion reflects various interpretations of the problem and the algebra involved.

Johnx1
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Farhan and Junhao had the same number of points in a game. After Farhan got another 470 points and Junhao got another 50 points, Farhan had 3 times as many points as Junhao. How many points did each of them have at first?

My answer:

Farhan = F
Junhao = J

We know F = H,
F = F + 470
J = J + 50
F = 3J

so then I did,

F + 470 = J + 50

3J + 470 = J + 50

J = -210.

Then I pluged it back into 3J + 470 = J + 50

so I get -160 = -160.

I'm not sure what I did wrong. Also, I know the answer is 160.
 
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Johnx said:
Farhan and Junhao had the same number of points in a game. After Farhan got another 470 points and Junhao got another 50 points, Farhan had 3 times as many points as Junhao. How many points did each of them have at first?

My answer:

Farhan = F
Junhao = J

We know F = H,

Okay, you are good up to here. So in fact we really only need one variable...let's let \(O\) by the number of points both originally had. So, next let's look at the statement:

After Farhan got another 470 points and Junhao got another 50 points, Farhan had 3 times as many points as Junhao.

After Farhan got another 470 points, his number of points is:

$$O+470$$

After Junhao got another 50 points, his number of points is:

$$O+50$$

And "Farhan had 3 times as many points as Junhao" then means we can write:

$$O+470=3(O+50)$$

We can now solve this equation to find \(O\), which is what the question asks us to find. What do you get?
 
MarkFL said:
let \(O\) by the number of points both originally had. So, next let's look at the statement:

After Farhan got another 470 points and Junhao got another 50 points, Farhan had 3 times as many points as Junhao.

After Farhan got another 470 points, his number of points is:

$$O+470$$

After Junhao got another 50 points, his number of points is:

$$O+50$$

And "Farhan had 3 times as many points as Junhao" then means we can write:

$$O+470=3(O+50)$$

We can now solve this equation to find \(O\), which is what the question asks us to find. What do you get?

So then I did:

F = H
F = O + 470
H = O + 50

We also know F = 3(J)O+470=3(O+50)

O = 160

Thank you.
 
Johnx said:
Farhan and Junhao had the same number of points in a game. After Farhan got another 470 points and Junhao got another 50 points, Farhan had 3 times as many points as Junhao. How many points did each of them have at first?

My answer:

Farhan = F
Junhao = J
Okay, good. However, I would have said "F is the number of points Farhan scored and J is the number of points[/g] Junhao scored. "Farhan" and "Junhao" are people[/g] not numbers!

We know F = H,
Where did "H" come from? Did you mean "J"?

F = F + 470
J = J + 50
No! you are using "F" to represent the number of points Farhan had initially. You cannot use the same letter to represent the number of points Farhan had later. And, algebraically, "F= F+ 470", subtracting "F" from both sides, gives 0= 470 which is certainly not true!

F = 3J
Rather F+ 470= 3(J+ 50)

so then I did,

F + 470 = J + 50

3J + 470 = J + 50

J = -210.

Then I pluged it back into 3J + 470 = J + 50

so I get -160 = -160.

I'm not sure what I did wrong. Also, I know the answer is 160.
You had, above, F+ 470= 3(J+ 50) but F= J so you can use just a single letter to represent that number- say F+ 470= 3(F+ 50)= 3F+ 150.

3F- F= 470- 150
2F= 320
F= 320/2= 160
 
Country Boy said:
No! you are using "F" to represent the number of points Farhan had initially. You cannot use the same letter to represent the number of points Farhan had later. And, algebraically, "F= F+ 470", subtracting "F" from both sides, gives 0= 470 which is certainly not true!

thank you for pointing that out :-)
 

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