Farhan and Junhao score points

• MHB
• Johnx1
In summary, 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. To find the initial number of points each had, we can set up the equation F+470=3(J+50) and solve for F, which is the number of points Farhan had initially. Simplifying, we get F+470=3F+150, and solving for F gives us F=160. Therefore, Farhan initially had 160 points and Junhao had 160 points as well.
Johnx1
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?

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.

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?

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:

$$\displaystyle O+470$$

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

$$\displaystyle O+50$$

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

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

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:

$$\displaystyle O+470$$

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

$$\displaystyle O+50$$

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

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

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?

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 :-)

1. How did Farhan and Junhao score points?

Farhan and Junhao scored points by participating in a game or competition and successfully completing tasks or challenges that were assigned to them. The specific details of how they scored points would depend on the rules and regulations of the specific game or competition.

2. Who is Farhan and Junhao?

Farhan and Junhao are two individuals who participated in a game or competition where points were awarded for completing tasks or challenges. They could be friends, teammates, or competitors, depending on the context of the game or competition.

3. How many points did Farhan and Junhao score?

The number of points that Farhan and Junhao scored would depend on their performance in the game or competition. They could have scored a few points or a significant amount, depending on their success in completing tasks and challenges.

4. What was the purpose of scoring points for Farhan and Junhao?

The purpose of scoring points for Farhan and Junhao was to determine their success and ranking in the game or competition. Points are often used as a way to keep track of progress and determine winners in competitions.

5. Was Farhan and Junhao's score enough to win the game or competition?

It depends on the specific rules and regulations of the game or competition. If their score was the highest among all the participants, then they would likely be considered the winners. However, if their score was not the highest, they may not have won the game or competition.

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