Question

For their CD collections, Alan, Tom, and Barbara have a total of 52 CD’s. If Barbara had 6 more, then she would have as many as both of the boys together. Tom has three more CD’s than Alan. How many CD’s does each of the three have?

Answer 1

We can write three equations using the given information.
Let A be the number of CDs that Alan has, T be Tom's number of CDs and B be Barbara's number of CDs.
A + T + B = 52 ..........(1)
B + 6 = A + T ............(2)
T - 3 = A ...................(3)
Do you follow, so far?

Answer 2

Yes:)

Answer 3

Do you have any ideas on how to solve these equations?

Answer 4

Breaking it down like that helped but I am still very lost when it comes to actually solving it.

Answer 5

One way to solve is to rearrange (2) as follows:
B + 6 = A + T ............(2)
Rearranging we get
A + T - B = 6 ............(4)
Now if we add equations (1) and (4) can you find the result?

Answer 6

Add these:
A + T + B = 52 ..........(1)
A + T - B = 6 ............(4)

Answer 7

So would A + T equal 46? Then would I just divide by two then take 3 from A and add it to T?

Answer 8

Adding (1) and (4) gives:
2A + 2T = 58 ...........(5)
Do you follow?

Answer 9

Oh, okay. Yes I'm following.

Answer 10

Equation (3) gives A in terms of T
A = T - 3
Therefore we can substitute for A in equation (5) giving:
2(T - 3) + 2T = 58 ..........(6)
Can you solve (6) to find the value of T?

Answer 11

So T=16?

Answer 12

Correct. Good work!
Now substitute your value for T into (3) to find the value of A:
T - 3 = A ...................(3)

Answer 13

A= 13
T=16
B=23

Correct?

Answer 14

Correct. Well done!

Answer 15

Alright, thank you so much for your help! :)

Answer 16

You're welcome :)