MHB Farhan and Junhao score points

[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?

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.

 

[MarkFL]

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?

 

[Johnx1]

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.

 

[HOI]

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

 

[Johnx1]

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 :-)