Question

Create the system of linear 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 for $4 and flowers for $5. The team captain estimates they will sell no more than 150 items, but they know that 50 flowers have already been preordered.(1 point)
Responses

4x+5y≥600
4
𝑥
+
5
𝑦
≥
600
, x+y≥150
𝑥
+
𝑦
≥
150
, y≤50
𝑦
≤
50
4 x plus 5 y greater-than-or-equal-to 600 , x plus y greater-than-or-equal-to 150 , y less-than-or-equal-to 50

4x+5y>600
4
𝑥
+
5
𝑦
>
600
, x+y≥150
𝑥
+
𝑦
≥
150
, y≥50
𝑦
≥
50
4 x plus 5 y greater than 600 , x plus y greater-than-or-equal-to 150 , y greater-than-or-equal-to 50

4x+5y≥600
4
𝑥
+
5
𝑦
≥
600
, x+y≤150
𝑥
+
𝑦
≤
150
, y≥50
𝑦
≥
50
4 x plus 5 y greater-than-or-equal-to 600 , x plus y less-than-or-equal-to 150 , y greater-than-or-equal-to 50

4x+5y≥600
4
𝑥
+
5
𝑦
≥
600

Answer 1

To model the situation with a system of linear inequalities, we need to consider the following points from the problem:

1. The team wants to raise at least $600.
2. They sell chocolate for $4 each (let's denote the number of chocolates sold as \(x\)).
3. They sell flowers for $5 each (let's denote the number of flowers sold as \(y\)).
4. They estimate selling no more than 150 items total.
5. They already have 50 flowers preordered.

From this information, we can derive the following inequalities:

1. **Revenue Inequality**: They want to raise at least $600, so:
\[
4x + 5y \geq 600
\]

2. **Total Items Inequality**: They estimate selling no more than 150 items. Since 50 flowers are already ordered, the number of items sold must not exceed \(150 - 50 = 100\):
\[
x + y \leq 100
\]

3. **Non-negativity**: Both \(x\) and \(y\) must be non-negative since they cannot sell a negative number of items:
\[
x \geq 0
\]
\[
y \geq 0
\]

Putting it all together, the system of inequalities is:
\[
\begin{align*}
1. & \quad 4x + 5y \geq 600 \\
2. & \quad x + y \leq 100 \\
3. & \quad x \geq 0 \\
4. & \quad y \geq 0 \\
\end{align*}
\]

None of the provided responses exactly represent this system, but based on the context, the inequalities should reflect the conditions outlined above. The last option is incomplete and does not specify the limitations on \(x\) and \(y\).

To clarify:
- There is no inequality \(y \leq 50\) or \(y \geq 50\) needed based on the information provided. We determined that they will sell a maximum of 100 items but already have orders for 50 flowers.
- So, in this case, we do not need to enforce those bounds directly.

Please ensure to choose the properties that reflect the conditions accurately.