1. **State the problem:** We need to find the maximum number of balloons that can be tied on a ribbon of length 180.5 cm, with each balloon spaced 8 cm apart.
2. **Understand the spacing:** If balloons are tied 8 cm apart, the distance between consecutive balloons is 8 cm.
3. **Calculate the number of intervals:** The number of intervals between balloons is one less than the number of balloons. Let $n$ be the number of balloons. Then the total length covered by the intervals is $8(n-1)$ cm.
4. **Set up the inequality:** The total length of the ribbon is 180.5 cm, so
$$8(n-1) \leq 180.5$$
5. **Solve for $n$:**
$$n-1 \leq \frac{180.5}{8}$$
$$n-1 \leq 22.5625$$
$$n \leq 23.5625$$
6. **Interpret the result:** Since $n$ must be an integer (number of balloons), the maximum number of balloons is
$$n = 23$$
**Final answer:** The most number of balloons that can be tied on the 180.5 cm ribbon with 8 cm spacing is **23**.
Balloons On Ribbon
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.