Tina is going to put 1 -inch square tiles on the picture frame shown at right. a. If the frame is one tile wide, how many 1 -inch square tiles will she need? b. Would more 1 -inch square tiles fit inside the

To solve the problem, we need to clarify the dimensions of the picture frame and the area that Tina is covering with the tiles. Since the dimensions of the frame are not provided, I will assume a general rectangular frame with an outer width and height, and an inner width and height that is reduced by the width of the frame. Let's denote: - \( W_o \): outer width of the frame - \( H_o \): outer height of the frame - \( W_i \): inner width of the frame (which is \( W_o - 2 \) since the frame is 1 tile wide on both sides) - \( H_i \): inner height of the frame (which is \( H_o - 2 \) since the frame is 1 tile wide on both sides) ### Part a: Number of Tiles Needed for the Frame 1. **Calculate the area of the outer frame**: \[ A_o = W_o \times H_o \] 2. **Calculate the area of the inner frame**: \[ A_i = W_i \times H_i = (W_o - 2) \times (H_o - 2) \] 3. **Calculate the area of the frame itself**: \[ A_f = A_o - A_i \] 4. **The number of 1-inch square tiles needed** is equal to the area of the frame: \[ \text{Number of tiles} = A_f \] ### Part b: Tiles that Fit Inside the Frame 1. **The number of 1-inch square tiles that fit inside the frame** is equal to the area of the inner frame: \[ \text{Number of tiles inside} = A_i \] Now, let's summarize the calculations. If you provide the specific dimensions for \( W_o \) and \( H_o \), I can perform the calculations to find the exact number of tiles needed for both parts.