Word Problem Help: "Ben and Anna each have some CDs...."

[cassie81]

"Ben and Anna each have some CDs. If Anna gives six of her CDs to Ben, he would then have twice as many CDs as Anna. If instead, Anna takes six Cds from Ben, then bother would have the same number of CDs. What is the total number of CDs that Ben and Anna have?

 

[Deleted member 4993]

"Ben and Anna each have some CDs. If Anna gives six of her CDs to Ben, he would then have twice as many CDs as Anna. If instead, Anna takes six Cds from Ben, then bother would have the same number of CDs. What is the total number of CDs that Ben and Anna have?

Start defining variables:

# of CDs Ben have now = B.....................# of CDs Anna have now = A

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

 

[cassie81]

Start defining variables:

# of CDs Ben have now = B.....................# of CDs Anna have now = A

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

I tried a = 16 b= 10, a=6 b = 6
i am stumped

 

[stapel]

"Ben and Anna each have some CDs. If Anna gives six of her CDs to Ben, he would then have twice as many CDs as Anna. If instead, Anna takes six Cds from Ben, then bother would have the same number of CDs. What is the total number of CDs that Ben and Anna have?

Start defining variables:

# of CDs Ben have now = B.....................# of CDs Anna have now = A

I tried a = 16 b= 10, a=6 b = 6
i am stumped

Leaving aside the change in case, how did you get that Ben now has both b = 10 and also b = 6 CDs? Especially since the exercise nowhere states how many they have now? Where did you get these numbers? From what source? By what logic?

Instead, try following the instructions:

. . .CDs now:
. . . . .Ben: b
. . . . .Anna: a

For the first swap, they end up with this:

. . .CDs after 1st swap:
. . . . .Ben: b + 6
. . . . .Anna: a - 6

. . .stated relationship after 1st swap:
. . . . .(Ben, after 1st swap) is (twice as many as)(Anna, after 1st swap)

Translate this English sentence into algebra. (here)

Now return them to their original position, and then apply the second swap ("instead" of the first swap). Do the same sort of translation. Create the same sort of equation.

You now have two equations in two unknowns. Solve the system for the values of the variables, using whatever method you prefer. (here) If you get stuck, please reply showing your thoughts and efforts so far. (Or, if you posted this to "Arithmetic" because you're in some course previous to algebra, please state your level of study.) Thank you!