Question

Tura has $60 to spend on new art supplies. Each marker costs $2 and each pencil costs $0.75. Tura wants to buy at least 2 times more pencils than markers. Write the system of inequalities that models the situation. Let x represent the number of markers she can buy, and let y represent the number of pencils she can buy.(1 point)
Responses

2x+0.75y≤60
2
𝑥
+
0.75
𝑦
≤
60
and x≥2y
𝑥
≥
2
𝑦
2 x plus 0.75 y less-than-or-equal-to 60 and x greater-than-or-equal-to 2 y

2x+0.75y≥60
2
𝑥
+
0.75
𝑦
≥
60
and y≥2x
𝑦
≥
2
𝑥
2 x plus 0.75 y greater-than-or-equal-to 60 and y greater-than-or-equal-to 2 x

2x+0.75y≤60
2
𝑥
+
0.75
𝑦
≤
60
and y≥2x
𝑦
≥
2
𝑥
2 x plus 0.75 y less-than-or-equal-to 60 and y greater-than-or-equal-to 2 x

x+y≤60
𝑥
+
𝑦
≤
60
and x≥2y

Answer 1

To model Tura's situation using inequalities, we have the following variables:

- Let \( x \) represent the number of markers.
- Let \( y \) represent the number of pencils.

From the given information, we can establish the following inequalities:

1. **Total cost constraint**: Since each marker costs $2 and each pencil costs $0.75, and Tura has $60 to spend, we write the inequality for the total spending:
\[
2x + 0.75y \leq 60
\]

2. **Pencil-to-marker ratio**: Tura wants to buy at least 2 times more pencils than markers, which can be written as:
\[
y \geq 2x
\]

3. **Non-negativity constraints**: Since Tura cannot buy a negative number of markers or pencils, we need to add:
\[
x \geq 0
\]
\[
y \geq 0
\]

Combining these inequalities, the complete system of inequalities modeling the situation is:

1. \( 2x + 0.75y \leq 60 \)
2. \( y \geq 2x \)
3. \( x \geq 0 \)
4. \( y \geq 0 \)

From the provided options, the correct response representing this scenario is:

**2x + 0.75y ≤ 60 and y ≥ 2x**