James looks in his TV cabinet and finds some old Beta and VHS tapes. He has 17 tapes in all. He finds that he has three more Beta tapes than VHS tapes. How many of each type does he have?

Let's denote the number of Beta tapes as \( B \) and the number of VHS tapes as \( V \). From the given information, we have two equations: 1. The total number of tapes is 17: \( B + V = 17 \) 2. There are three more Beta tapes than VHS tapes: \( B = V + 3 \) We can solve this system of equations to find the values of \( B \) and \( V \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}B+V=17\\B=V+3\end{array}\right.\) - step1: Substitute the value of \(B:\) \(V+3+V=17\) - step2: Add the terms: \(2V+3=17\) - step3: Move the constant to the right side: \(2V=17-3\) - step4: Subtract the numbers: \(2V=14\) - step5: Divide both sides: \(\frac{2V}{2}=\frac{14}{2}\) - step6: Divide the numbers: \(V=7\) - step7: Substitute the value of \(V:\) \(B=7+3\) - step8: Simplify: \(B=10\) - step9: Calculate: \(\left\{ \begin{array}{l}B=10\\V=7\end{array}\right.\) - step10: Check the solution: \(\left\{ \begin{array}{l}B=10\\V=7\end{array}\right.\) - step11: Rewrite: \(\left(B,V\right) = \left(10,7\right)\) By solving the system of equations, we find that James has 10 Beta tapes and 7 VHS tapes in his TV cabinet.