Subjects algebra

Balloons On Ribbon

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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**.