Help translating word problem: "Carlos began with twice as much money as David had."

[falcios]

Help translating word problem: "Carlos began with twice as much money as David had."

Carlos began with twice as much money as David had.
After Carlos gave $12 to David, Carlos still had $10 more than David.
How much money did they have combined at the start
The correct answer is
Let x=the number of dollars David had to start
If Carlos started with twice as much money as David then Carlos started with 2x dollars. After Carlos gave David $12, Carlos had 2x-12 dollars and David had x + 12 dollars. If Carlos still had $10 more than David, then
2x - 12 = 10 + x +12

Question:
If Carlos still had $10 more than David, why is it specified to the right of the equal sign in David’s expression and not with Carlos expression?



Thanks in advance.

 

[Deleted member 4993]

Carlos began with twice as much money as David had.
After Carlos gave $12 to David, Carlos still had $10 more than David.
How much money did they have combined at the start
The correct answer is
Let x=the number of dollars David had to start
If Carlos started with twice as much money as David then Carlos started with 2x dollars. After Carlos gave David $12, Carlos had 2x-12 dollars and David had x + 12 dollars. If Carlos still had $10 more than David, then
2x - 12 = 10 + x +12 Question:If Carlos still had $10 more than David, why is it specified to the right of the equal sign in David’s expression and not with Carlos expression?
Thanks in advance.

After $12 changing hand - we know that:

[Carlos's money] - [Davids money] = 10

[2x - 12] - [x +12] = 10

[2x - 12] = [x + 12] + 10

continue.....

 

[Steven G]

Carlos began with twice as much money as David had.
After Carlos gave $12 to David, Carlos still had $10 more than David.
How much money did they have combined at the start
The correct answer is
Let x=the number of dollars David had to start
If Carlos started with twice as much money as David then Carlos started with 2x dollars. After Carlos gave David $12, Carlos had 2x-12 dollars and David had x + 12 dollars. If Carlos still had $10 more than David, then
2x - 12 = 10 + x +12

Question:
If Carlos still had $10 more than David, why is it specified to the right of the equal sign in David’s expression and not with Carlos expression?



Thanks in advance.

Carlos has $10 more dollars than David. Say Carlos has $30 and David has $20 (note that Carlos has $10 more than David). Now we want to make an equation which has an equal sign. So what is on both sides of the equal sign MUST be equal.

$30 \(\displaystyle \neq\)$20. But if add $10 to David's side then we will have equality! That is $30 = $20 + $10.

Now you might wonder where Carlos' extra $10 is. Well $30 = $20 + $10.

 

[HallsofIvy]

Here is how I would do this. Let C be the amount of money Carl has initially, D the amount of money David had

Carlos began with twice as much money as David had.

So C= 2D

After Carlos gave $12 to David, Carlos still had $10 more than David.

After Carlos gives $12 to David, Carlos has C- 12, David has D+ 12.
So now C- 12= D+ 12+ 10=D+ 22, which, adding 12 to both sides, is the same as C= D+ 34.
Solve the two equations C= D+ 34 and C= 2D. 2D= D+ 34 because each is equal to C. Subtracting D from both sides, D= 34. Since C= 2D, C= 2(34)= 68. Carlos initially had $68 and David had $34.

Check. $68 is twice $34. If Carlos gives $12 to David, he will have $68- 12= $56 and David will have $34+ 12= $46. Carlos still has $10 more than David.

How much money did they have combined at the start
The correct answer is
Let x=the number of dollars David had to start
If Carlos started with twice as much money as David then Carlos started with 2x dollars. After Carlos gave David $12, Carlos had 2x-12 dollars and David had x + 12 dollars. If Carlos still had $10 more than David, then
2x - 12 = 10 + x +12

Well, that's not yet "the correct answer" because it is not an answer! It is an equation you can use to find the correct answer.

Question:
If Carlos still had $10 more than David, why is it specified to the right of the equal sign in David’s expression and not with Carlos expression? Thanks in advance.

If "Carlos still had $10 more than David" then then the amount Carlos has is "the amount David has plus 10".

If David has $20 then Carlos has $10 more: 20+ 10= $30. The $10 is added to David's money o equal Carlos' money.

 

[falcios]

Thanks

Thanks HallsofIvy and Jomo for your responses.

I never heard it explained this way before. I think I got it.

Here is how I would do this. Let C be the amount of money Carl has initially, D the amount of money David had


So C= 2D


After Carlos gives $12 to David, Carlos has C- 12, David has D+ 12.
So now C- 12= D+ 12+ 10=D+ 22, which, adding 12 to both sides, is the same as C= D+ 34.
Solve the two equations C= D+ 34 and C= 2D. 2D= D+ 34 because each is equal to C. Subtracting D from both sides, D= 34. Since C= 2D, C= 2(34)= 68. Carlos initially had $68 and David had $34.

Check. $68 is twice $34. If Carlos gives $12 to David, he will have $68- 12= $56 and David will have $34+ 12= $46. Carlos still has $10 more than David.


Well, that's not yet "the correct answer" because it is not an answer! It is an equation you can use to find the correct answer.


If "Carlos still had $10 more than David" then then the amount Carlos has is "the amount David has plus 10".

If David has $20 then Carlos has $10 more: 20+ 10= $30. The $10 is added to David's money o equal Carlos' money.