To determine how many attempts it will take for the monkey to climb 10 meters of the pole, let's break down the process step-by-step.
1. Understand the problem:
- The pole height is 15 meters.
- The monkey's target is to climb up to 10 meters.
- In each attempt, the monkey climbs 3 meters but then slips down 2 meters.
2. Effective progress per attempt:
- Each attempt consists of a 3-meter climb followed by a 2-meter slip. Therefore, the effective distance the monkey climbs after each attempt is [tex]\(3 - 2 = 1\)[/tex] meter.
3. Reaching as close to 10 meters as possible without passing it:
- If the effective distance per attempt is 1 meter, it will take:
[tex]\[
\text{Number of complete attempts} = \frac{10 - 1}{1} = 9
\][/tex]
This means the monkey will have climbed 9 meters after 9 attempts.
4. Remaining distance to cover:
- After 9 attempts, the monkey is at 9 meters.
- It needs only 1 more meter to reach 10 meters.
5. Final attempt:
- On the next (10th) attempt, the monkey climbs 3 meters.
- After reaching 10 meters, it doesn’t matter if it slips since it has already reached or surpassed the 10-meter mark.
6. Conclusion:
- Therefore, the total number of attempts required for the monkey to climb 10 meters of the pole is 10 attempts.
So, the monkey will be able to climb 10 meters of the pole in 10 attempts.
