Questions: Design stencil. A stencil of Pennsylvania Dutch designs consists of a tulip, a wheel of fortune, a pomegranate, a peacock, and a heart. Each figure on the stencil is 4 centimeters wide. You are decorating a day care center and you wish to stencil the designs near the top edge of a wall in a hallway that measures 1468 centimeters long. If you stencil the figures in the order indicated until you run out of room, what will be the last figure you stencil?

Solution Steps

To determine the last figure you stencil, first calculate the total width of one complete cycle of the stencil designs. Since each figure is 4 centimeters wide and there are 5 figures, the total width of one cycle is \(5 \times 4 = 20\) centimeters. Next, divide the total length of the wall (1468 centimeters) by the width of one cycle (20 centimeters) to find out how many complete cycles fit on the wall. The remainder of this division will tell you how many additional figures can be stenciled after the last complete cycle. Use this remainder to determine the last figure.

Each figure on the stencil is 4 centimeters wide, and there are 5 figures in total. Therefore, the width of one complete cycle of the stencil designs is calculated as follows: \[ \text{cycle\_width} = 5 \times 4 = 20 \text{ cm} \]

The total length of the wall is 1468 centimeters. To find out how many complete cycles of the stencil designs fit on the wall, divide the total length by the width of one cycle: \[ \text{complete\_cycles} = \left\lfloor \frac{1468}{20} \right\rfloor = 73 \]

After stenciling 73 complete cycles, calculate the remaining length of the wall that can be used for additional figures: \[ \text{remainder} = 1468 \mod 20 = 8 \text{ cm} \]

The remainder of 8 centimeters allows for additional figures to be stenciled. Since each figure is 4 centimeters wide, calculate how many additional figures can fit: \[ \text{last\_figure\_index} = \left\lfloor \frac{8}{4} \right\rfloor = 2 \] The figures are stenciled in the order: tulip, wheel of fortune, pomegranate, peacock, heart. The index 2 corresponds to the "pomegranate."

Final Answer