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?

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: \(x=8\)