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anonymous

  • one year ago

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?

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  1. kropot72
    • one year ago
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    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?

  2. anonymous
    • one year ago
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    Yes:)

  3. kropot72
    • one year ago
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    Do you have any ideas on how to solve these equations?

  4. anonymous
    • one year ago
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    Breaking it down like that helped but I am still very lost when it comes to actually solving it.

  5. kropot72
    • one year ago
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    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?

  6. kropot72
    • one year ago
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    Add these: A + T + B = 52 ..........(1) A + T - B = 6 ............(4)

  7. anonymous
    • one year ago
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    So would A + T equal 46? Then would I just divide by two then take 3 from A and add it to T?

  8. kropot72
    • one year ago
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    Adding (1) and (4) gives: 2A + 2T = 58 ...........(5) Do you follow?

  9. anonymous
    • one year ago
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    Oh, okay. Yes I'm following.

  10. kropot72
    • one year ago
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    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?

  11. anonymous
    • one year ago
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    So T=16?

  12. kropot72
    • one year ago
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    Correct. Good work! Now substitute your value for T into (3) to find the value of A: T - 3 = A ...................(3)

  13. anonymous
    • one year ago
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    A= 13 T=16 B=23 Correct?

  14. kropot72
    • one year ago
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    Correct. Well done!

  15. anonymous
    • one year ago
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    Alright, thank you so much for your help! :)

  16. kropot72
    • one year ago
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    You're welcome :)

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