Questions: Use the drawing tools to form the correct answer on the graph. A sports camp has a total of 2,880 to purchase new equipment. They need baseballs and baseball gloves. A pack of baseballs costs 16, and a glove costs 48. The camp needs to include at least 50 items in its order. Let x represent the number of gloves and y represent the number of packs of baseballs. Draw a graph, including four boundary lines and four shaded regions, to represent the number of packs of baseballs and baseball gloves the camp can purchase with its budget.

Use the drawing tools to form the correct answer on the graph. A sports camp has a total of 2,880 to purchase new equipment. They need baseballs and baseball gloves. A pack of baseballs costs 16, and a glove costs 48. The camp needs to include at least 50 items in its order. Let x represent the number of gloves and y represent the number of packs of baseballs. Draw a graph, including four boundary lines and four shaded regions, to represent the number of packs of baseballs and baseball gloves the camp can purchase with its budget.
Transcript text: Use the drawing tools to form the correct answer on the graph. A sports camp has a total of $\$ 2,880$ to purchase new equipment. They need baseballs and baseball gloves. A pack of baseballs costs $\$ 16$, and a glove costs $\$ 48$. The camp needs to include at least 50 items in its order. Let $x$ represent the number of gloves and $y$ represent the number of packs of baseballs. Draw a graph, including four boundary lines and four shaded regions, to represent the number of packs of baseballs and baseball gloves the camp can purchase with its budget.
failed

Solution

failed
failed

Solution Steps

Step 1: Define the equations

The total cost equation is: \[ 16y + 48x \leq 2880 \]

The total number of items equation is: \[ x + y \geq 50 \]

Step 2: Solve for y in terms of x

From the cost equation: \[ 16y + 48x \leq 2880 \] \[ y \leq \frac{2880 - 48x}{16} \] \[ y \leq 180 - 3x \]

From the items equation: \[ x + y \geq 50 \] \[ y \geq 50 - x \]

Step 3: Define the boundary lines

The boundary lines are:

  1. \( y = 180 - 3x \)
  2. \( y = 50 - x \)
  3. \( x = 0 \)
  4. \( y = 0 \)

Final Answer

The inequalities are: \[ y \leq 180 - 3x \] \[ y \geq 50 - x \] \[ x \geq 0 \] \[ y \geq 0 \]

{"axisType": 3, "coordSystem": {"xmin": 0, "xmax": 100, "ymin": 0, "ymax": 200}, "commands": ["y = 180 - 3x", "y = 50 - x", "x = 0", "y = 0"], "latex_expressions": ["$y = 180 - 3x$", "$y = 50 - x$", "$x = 0$", "$y = 0$"]}

Was this solution helpful?
failed
Unhelpful
failed
Helpful