need help with word problem

[mathbot]

The team scored 28 points in their game on friday. They scored twice as many 2-pointers as 3-pointers. How many 2-pointers did they score?

I can tell it's a multiplication problem (twice as many). they totaled 28 points but 2 times more 2 pointers. is it correct to say that 28=2x, which would lead to an answer of 14, but that's 1/2 of the total and doesn't answer the question.
or is it 28 = 2x + x which is 28=3x. but then that would leave a remainder and still doesn't answer the question.

Can someone explain the process for solving this?

 

[Deleted member 4993]

The team scored 28 points in their game on friday. They scored twice as many 2-pointers as 3-pointers. How many 2-pointers did they score?

I can tell it's a multiplication problem (twice as many). they totaled 28 points but 2 times more 2 pointers. is it correct to say that 28=2x, which would lead to an answer of 14, but that's 1/2 of the total and doesn't answer the question. Can someone explain the process for solving this?

The FIND of the problem is - How many 2-pointers did they score?

Let the

number of 2-pointers scored = W​

​

number of 3-pointers scored = H​

I am going to assume something that is not stated explicitly in the problem-statement:

I assume that only 2-pointers and 3-pointers have been scored in the game.​

Then we have:

"They scored twice as many 2-pointers as 3-pointers" \(\displaystyle \to\)
W = 2 * H ........Given ...................(1)............and

"The team scored 28 points in their game" \(\displaystyle \to\) 2 * W + 3 * H = 28 ........................Given ...................(2)

Substituting (1) in (2) ..................................\(\displaystyle \to\) 2 * (2 * H) + 3 * H = 28.......\(\displaystyle \to\) ......H = ?...W = ?... continue

 

[Otis]

is it correct to say that 28=2x

Hi mathbot. What would be your definition for x, above? (It can't be the number of baskets made because some shots count more than others.)

or is it 28 = 2x + x

Again, what is your definition for symbol x, in that equation?

It's best to write down the meaning for symbols that you choose, before writing equations. Doing so makes it easier to tell whether your equations make sense.

There are two types of shots: 2-pointers and 3-pointers. So, how about starting with two symbols.

X = number of 3-point shots made

x = number of 2-point shots made

Now, try writing some equations. For example, how is x related to X?



[imath]\;[/imath]

 

[mathbot]

"The team scored 28 points in their game" \displaystyle \to→ 2 * W + 3 * H = 28 ........................Given ...................(2)

How did you plug those numbers in to come to that? Could you break that down for me? That's the part that confuses me about word problems is when it comes to actually plugging everything in. If I hadn't seen what you did I think I would have come up with something that looks completely different... and wrong.

 

[Deleted member 4993]

"The team scored 28 points in their game" \displaystyle \to→ 2 * W + 3 * H = 28 ........................Given ...................(2)

How did you plug those numbers in to come to that? Could you break that down for me? That's the part that confuses me about word problems is when it comes to actually plugging everything in. If I hadn't seen what you did I think I would have come up with something that looks completely different... and wrong.

According to my assumption:

How many two-pointers were recorded in the game? \(\displaystyle \to \) = W​

​

How many points were scored, in the game, with those two pointers? \(\displaystyle \to \) = 2*W​

Did you understand the two lines written above?

If yes - then write similar statements about 3-pointers.

If no - tell us exactly which part/s of those two statements escapes your comprehension?

 

[Steven G]

Let w = # of 2-pointers and h = # of 3-pointers
twice as many 2-pointers as 3-pointers.
Twice as many translates to 2 times and as translates to =
Now translate twice as many 2-pointers as 3-pointers
2*h=w

 

[Dr.Peterson]

Let w = # of 2-pointers and h = # of 3-pointers
twice as many 2-pointers as 3-pointers.
Twice as many translates to 2 times and as translates to =
Now translate twice as many 2-pointers as 3-pointers
2*h=w

Why is the variable for 3-pointers in blue, along with the word "2-pointers"? I think that's a little confusing, though your equation is correct.

I like to first restate "there are twice as many 2-pointers as 3-pointers" as "the number of 2-pointers is twice the number of 3-pointers" before translating to symbols. Untangle the English before doing the math part; English is bad enough.

 

[Steven G]

Why is the variable for 3-pointers in blue, along with the word "2-pointers"? I think that's a little confusing, though your equation is correct.

I like to first restate "there are twice as many 2-pointers as 3-pointers" as "the number of 2-pointers is twice the number of 3-pointers" before translating to symbols. Untangle the English before doing the math part; English is bad enough.

Thank you.

 

[mdhannan]

The team scored 28 points in their game on friday. They scored twice as many 2-pointers as 3-pointers. How many 2-pointers did they score?

I can tell it's a multiplication problem (twice as many). they totaled 28 points but 2 times more 2 pointers. is it correct to say that 28=2x, which would lead to an answer of 14, but that's 1/2 of the total and doesn't answer the question.
or is it 28 = 2x + x which is 28=3x. but then that would leave a remainder and still doesn't answer the question.

Can someone explain the process for solving this?

Let x be the number of 2-pointers and y be the number 3-pointers
So, 1 time 2-pointers= 2 points and 1 time 3-pointers= 3 points.
therefore, x times 2-pointers= 2x points and y times 3-pointers= 3y points.
∴, 2x+3y=28...(1)
x=2y...........(2)
2*2y+3y=28 ->y=4
x=2*4=8

 

[Deleted member 4993]

Let x be the number of 2-pointers and y be the number 3-pointers
So, 1 time 2-pointers= 2 points and 1 time 3-pointers= 3 points.
therefore, x times 2-pointers= 2x points and y times 3-pointers= 3y points.
∴, 2x+3y=28...(1)
x=2y...........(2)
2*2y+3y=28 ->y=4
x=2*4=8

Please do NOT FORGET to check your answers.