Certainly. Let's break down the problem step by step:
1. Understand the given inequality:
The inequality \(0.75C + 1.25A \leq 7\) shows the total time spent by Horace on haircuts each day, where \(C\) is the number of child haircuts and \(A\) is the number of adult haircuts.
2. Determine the specific values provided:
We are given that \(C = 5\), meaning Horace gave 5 child haircuts today. We need to find the maximum number of adult haircuts \(A\) he can give with the remaining time.
3. Calculate the total time spent on child haircuts:
Each child haircut takes 0.75 hours. Thus, the time spent on 5 child haircuts is:
[tex]\[
0.75 \times 5 = 3.75 \text{ hours}
\][/tex]
4. Determine the remaining time available for adult haircuts:
The total available time for haircuts is 7 hours. Subtract the time spent on child haircuts from this total to find the remaining time:
[tex]\[
7 - 3.75 = 3.25 \text{ hours}
\][/tex]
5. Calculate the maximum number of adult haircuts possible:
Each adult haircut takes 1.25 hours. To find the maximum number of adult haircuts Horace can give with the remaining 3.25 hours, we divide the remaining time by the time required for one adult haircut:
[tex]\[
\frac{3.25}{1.25} = 2.6
\][/tex]
Thus, the maximum number of adult haircuts Horace can give with the remaining time is 2.6. Since Horace cannot give a fraction of a haircut, he can give up to 2 adult haircuts.
Summary:
- Time spent on child haircuts: 3.75 hours
- Remaining time for adult haircuts: 3.25 hours
- Maximum number of adult haircuts possible: 2.6 (or 2 when considering whole haircuts)
Therefore, under the given conditions, the most number of adult haircuts Horace can give with the remaining time is 2.
