Question

Create the system of inequalities that models the following situation. The field hockey team at school is hosting a fundraiser. They hope to raise at least $600. They are selling chocolate bars for $4 each and flowers for $5 each. The team captain estimates they will sell no more than 150 items. What are the two equations that model the situation? Let x represent the number of chocolate bars, and let y represent the number of flowers sold.(1 point) Responses 4x+5y>600 and x+y<150 4 x plus 5 y greater than 600 and x plus y is less than 150 4x+5y≤600 and x+y<150 4 x plus 5 y less-than-or-equal-to 600 and x plus y less than 150 5x+4y≤150 and x−y>150 5 x plus 4 y less-than-or-equal-to 150 and x minus y greater-than 150 4x+5y≥600 and

Answer 1

To model the situation of the field hockey team's fundraiser, you have the following conditions:

1. They want to raise at least $600.
2. They will sell a maximum of 150 items (chocolate bars and flowers combined).

Let's define the variables:
- Let \( x \) represent the number of chocolate bars sold.
- Let \( y \) represent the number of flowers sold.

Based on the above conditions, we can set up the following inequalities:

1. To represent the goal of raising at least $600, we have:
\[
4x + 5y \geq 600
\]

2. To represent the limit on the total number of items sold (no more than 150), we have:
\[
x + y \leq 150
\]

Thus, the correct system of inequalities modeling the situation is:

\[
\begin{cases}
4x + 5y \geq 600 \\
x + y \leq 150
\end{cases}
\]

Among the responses provided, this corresponds to:
**4x + 5y ≥ 600 and x + y ≤ 150**.