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)

Question

Responses

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

4
x
+
5
y
>
600
,
x
+
y
≥
150
,
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

4
x
+
5
y
≥
600
,
x
+
y
≤
150
,
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

4
x
+
5
y
≥
600
,
x
+
y
≥
150
,
y
≤
50

Answer 1

To model the situation described, we need to set up a system of linear inequalities based on the information given.

Let:

• \( x \) = number of chocolate items sold
• \( y \) = number of flower items sold

From the problem, we have the following conditions:

1. The team hopes to raise at least $600 from chocolate and flowers: \[ 4x + 5y \geq 600 \]

2. The team estimates they will sell no more than 150 items in total: \[ x + y \leq 150 \]

3. They already have 50 flowers preordered, so the number of flowers sold must be at least 50: \[ y \geq 50 \]

So the correct system of inequalities that models the situation is:

\[ 4x + 5y \geq 600 \] \[ x + y \leq 150 \] \[ y \geq 50 \]

Among the options given, the correct one is:

4 x + 5 y ≥ 600, x + y ≤ 150, y ≥ 50