Joseph is going to paint the panels of a fence. He is going to use the same repeating pattern for the entire fence. The rule is "orange, yellow, pink, green, purple." If there are 98 panels in the fence, how many will be painted green? Enter your answer in the box.

Question

(1 point)
There will be green panels.

Answer 1

To determine how many panels will be painted green, we need to analyze the repeating pattern: "orange, yellow, pink, green, purple."

This pattern has a total of 5 colors. We need to find out how many complete cycles of this pattern fit into 98 panels.

1. Determine how many complete cycles fit into 98: \[ \text{Number of complete cycles} = \frac{98}{5} = 19.6 \] Since we can only have complete cycles, we take the whole number part, which is 19.

2. Calculate the total number of panels in complete cycles: \[ \text{Total panels in complete cycles} = 19 \times 5 = 95 \]

3. Determine how many panels are left after complete cycles: \[ \text{Remaining panels} = 98 - 95 = 3 \]

4. Identify the position of colors in the pattern: The colors for the first 5 panels are:

   1. Orange
   2. Yellow
   3. Pink
   4. Green
   5. Purple

   The remaining panels will take the colors:

   • 96th panel: Orange
   • 97th panel: Yellow
   • 98th panel: Pink

5. Count how many panels are painted green: In each complete cycle of 5 colors, there is exactly 1 green panel. Hence, for 19 complete cycles, the number of green panels is: \[ \text{Green panels from complete cycles} = 19 \]

   There are no additional green panels in the remaining 3 panels (96th to 98th).

6. Final count of green panels: \[ \text{Total green panels} = 19 + 0 = 19 \]

Thus, the answer is: \[ \boxed{19} \]