18. Music Marc has 45 CDs in his collection, and Corinna has 61. If Marc buys 4 new CDs each month and Corinna buys 2 new CDs each month, after how many months will Marc and Corinna have the same number of CDs?

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To solve this problem, we need to find out after how many months Marc and Corinna will have the same number of CDs.

Let's denote the number of months as $$ x $$.

Marc starts with 45 CDs and buys 4 new CDs each month, so after $$ x $$ months, he will have:
$$ 45 + 4x $$ CDs.

Corinna starts with 61 CDs and buys 2 new CDs each month, so after $$ x $$ months, she will have:
$$ 61 + 2x $$ CDs.

We want to find out when Marc and Corinna will have the same number of CDs, so we set up the equation:
$$ 45 + 4x = 61 + 2x $$

Now, we can solve this equation to find the value of $$ x $$, which represents the number of months it will take for Marc and Corinna to have the same number of CDs.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$45+4x=61+2x$$
- step1: Move the expression to the left side:
  $$4x-2x=61-45$$
- step2: Add and subtract:
  $$2x=61-45$$
- step3: Add and subtract:
  $$2x=16$$
- step4: Divide both sides:
  $$\frac{2x}{2}=\frac{16}{2}$$
- step5: Divide the numbers:
  $$x=8$$
After 8 months, Marc and Corinna will have the same number of CDs.

18. Music Marc has 45 CDs in his collection, and Corinna has 61. If Marc buys 4 new CDs each month and Corinna buys 2 new CDs each month, after how many months will Marc and Corinna have the same number of CDs?

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