Let's break down the problem step by step:
1. Determine the total time available: Horace has 7 hours available for giving haircuts.
2. Time required for each type of haircut:
- Each child haircut takes 0.75 hours.
- Each adult haircut takes 1.2 hours.
3. Number of child haircuts given: Horace gave 5 child haircuts.
4. Calculate the total time spent on child haircuts:
- Each child haircut takes 0.75 hours.
- If Horace gave 5 child haircuts, the total time spent is:
[tex]\[
\text{Time spent on child haircuts} = 0.75 \times 5 = 3.75 \text{ hours}
\][/tex]
5. Calculate the remaining time available:
- Subtract the time spent on child haircuts from the total available hours:
[tex]\[
\text{Remaining hours} = \text{Total hours} - \text{Time spent on child haircuts} = 7 - 3.75 = 3.25 \text{ hours}
\][/tex]
6. Determine the maximum number of adult haircuts possible with the remaining time:
- Each adult haircut takes 1.2 hours.
- To find how many adult haircuts can be done in the remaining time, divide the remaining time by the time required for one adult haircut:
[tex]\[
\text{Maximum number of adult haircuts} = \left\lfloor \frac{3.25}{1.2} \right\rfloor
\][/tex]
- Performing the division:
[tex]\[
\frac{3.25}{1.2} \approx 2.71
\][/tex]
- Since the number of haircuts must be an integer, we take the floor value (i.e., the largest integer less than or equal to 2.71), which gives:
[tex]\[
\left\lfloor 2.71 \right\rfloor = 2
\][/tex]
Hence, Horace can give at most 2 adult haircuts with the remaining time.
Therefore, the correct answer is:
(B) Horace can give at most 2 adult haircuts.
