Lin and Ann each have a collection of music CDs.

If Ann gives Lin 12 of her CD's, they would each have the same amount of CDs.

If Lin gives Ann 12 of her CD's. Ann would have four times as many CDs as Lin.

How many music CD's does Ann have?

(A) 80 (B) 52 (C) 28 (D) 24

I have been stumped by this question. I have tried to solve this problem by simultaneous substitution. By that I mean, I made the 2 equations representing what has happened. (1) A = L + 12, (2) 4A = L - 12. From there I solved for Ann and got the answer 24. After checking the answer, I found that the answer was wrong and that the correct answer is in fact 52. I do not know any other way of approaching this other than trial and error (which I am not the biggest fan of).

If anyone has a simplified and accurate way of solving this, please reply. THANK YOU :)

  • $\begingroup$ Remember that if Ann gives Lee 12 CDs, not only does Lee gain 12 CDs but also Ann loses 12 CDs. With that in mind, your method should lead to a valid answer. $\endgroup$ – PattuX Nov 24 '17 at 1:39
  • $\begingroup$ that would mean the equations would become 1) (A-12) = (L+12) and 2) 4(A+12) = (l-12)... When solved the answer equals 28. which is wrong. Do you possibly have any other approaches? $\endgroup$ – progress Nov 24 '17 at 1:55
  • $\begingroup$ 28 is the correct result for L then. The corrospoinding solution for A is indeed 52. $\endgroup$ – PattuX Nov 24 '17 at 2:01
  • $\begingroup$ the problem with my equations was that I was assuming Lin has 4 times as many CDs as Ann. Whereas in reality... Ann has 4 times as CDs as Lin. Making the equation A +12 = 4(L-12). $\endgroup$ – progress Nov 24 '17 at 10:07
  • $\begingroup$ If you have a solution now, let me encourage you to write it up and post it as an answer. $\endgroup$ – Gerry Myerson Nov 24 '17 at 11:44
  1. we know that when A gives 12 CD's, L has the same amount as Ann when Lin is given 12 CDs.

  2. We know that when L gives 12 CD's, A has the 4 times the amount of Cd's then Ann when given 12 CDs.

Puting 1 and 2 into equations:

  1. A - 12 = L + 12
  2. A + 12 = 4(L-12)

Solve for L using the simultaneous equations method. therefore,

  1. L = 28

substitute 3. into 1, to solve for A, therefore, we get

  1. A = 52. the correct answer

Thus, the correct answer is B.


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