Answer :
To solve this problem, we need to figure out how many flower arrangements the homecoming committee can buy given their budget constraints. Let's go through the steps:
1. Understand the Total Budget Constraint:
- The committee has a total budget of [tex]$400.
2. Consider the Costs:
- Each flower arrangement costs $[/tex]9.
- There is also a delivery fee of $50.
3. Set Up the Inequality:
- The total cost of the flower arrangements plus the delivery fee must be less than or equal to the budget.
- The inequality will be: [tex]\(9f + 50 \leq 400\)[/tex], where [tex]\(f\)[/tex] represents the number of flower arrangements.
4. Solve the Inequality:
- First, subtract the delivery fee from the total budget to see how much can be spent on flower arrangements alone:
[tex]\[
400 - 50 = 350
\][/tex]
- Now, divide the remaining budget by the cost per arrangement to find out the maximum number of arrangements:
[tex]\[
\frac{350}{9} = 38.888\ldots
\][/tex]
- Since [tex]\(f\)[/tex] must be a whole number (you can't buy a fraction of a flower arrangement), round down to the nearest whole number:
[tex]\[
f = 38
\][/tex]
5. Conclusion:
- The maximum number of flower arrangements the committee can buy is 38.
Therefore, the correct inequality representing the number of flower arrangements the committee can purchase is [tex]\(f \leq 38\)[/tex], which corresponds to option D.
1. Understand the Total Budget Constraint:
- The committee has a total budget of [tex]$400.
2. Consider the Costs:
- Each flower arrangement costs $[/tex]9.
- There is also a delivery fee of $50.
3. Set Up the Inequality:
- The total cost of the flower arrangements plus the delivery fee must be less than or equal to the budget.
- The inequality will be: [tex]\(9f + 50 \leq 400\)[/tex], where [tex]\(f\)[/tex] represents the number of flower arrangements.
4. Solve the Inequality:
- First, subtract the delivery fee from the total budget to see how much can be spent on flower arrangements alone:
[tex]\[
400 - 50 = 350
\][/tex]
- Now, divide the remaining budget by the cost per arrangement to find out the maximum number of arrangements:
[tex]\[
\frac{350}{9} = 38.888\ldots
\][/tex]
- Since [tex]\(f\)[/tex] must be a whole number (you can't buy a fraction of a flower arrangement), round down to the nearest whole number:
[tex]\[
f = 38
\][/tex]
5. Conclusion:
- The maximum number of flower arrangements the committee can buy is 38.
Therefore, the correct inequality representing the number of flower arrangements the committee can purchase is [tex]\(f \leq 38\)[/tex], which corresponds to option D.
