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 first note the repeating pattern of colors: "orange, yellow, pink, green, purple."

This pattern consists of 5 colors. We can calculate how many complete cycles of the pattern fit into 98 panels, as well as how many extra panels are left over after the complete cycles.

1. Calculate the complete cycles: \[ \text{Number of complete cycles} = \left\lfloor \frac{98}{5} \right\rfloor = 19 \]

2. Calculate the number of panels painted in these complete cycles: In each complete cycle of 5 panels, each color (including green) is painted exactly once. So, the panels painted green in the complete cycles: \[ \text{Panels painted green in complete cycles} = 19 \times 1 = 19 \]

3. Calculate the remaining panels after the complete cycles: \[ \text{Remaining panels} = 98 \mod 5 = 3 \]

4. Determine how many of the remaining panels are green: The first three panels in the cycle pattern are "orange, yellow, pink," which means no extra green panels are painted in the remaining panels.

5. Total green panels: \[ \text{Total green panels} = 19 + 0 = 19 \]

Thus, the number of panels painted green is:

\[ \boxed{19} \]