Question

1. (04.05 mc)

ryleigh received a $50 gift card to the frozen yogurt shop for her birthday. the shop sells yogurt sundaes for $4 and yogurt cones for $3. how many sundaes and cones can she buy with her card?
if x represents the number of yogurt sundaes and y represents the number of yogurt cones, which graph correctly shows the solution to the problem ( 4x + 3y leq 50 )? (1 point)

Explanation:

Step1: Analyze the inequality

The inequality is \(4x + 3y\leq50\), where \(x\) is the number of sundaes (\(\$4\) each) and \(y\) is the number of cones (\(\$3\) each), and the total cost must be at most \(\$50\). First, find the intercepts to graph the boundary line \(4x + 3y = 50\).

Step2: Find x - intercept

Set \(y = 0\): \(4x=50\Rightarrow x=\frac{50}{4}=12.5\). So the x - intercept is \((12.5,0)\).

Step3: Find y - intercept

Set \(x = 0\): \(3y = 50\Rightarrow y=\frac{50}{3}\approx16.67\). So the y - intercept is \((0,\frac{50}{3})\).

Step4: Determine the line type and shading

Since the inequality is \(\leq\), the boundary line \(4x + 3y = 50\) is solid. We shade the region below the line (because for a test point like \((0,0)\), \(4(0)+3(0)=0\leq50\), which is true, so we shade the region containing \((0,0)\)). Also, \(x\) and \(y\) represent the number of sundaes and cones, so \(x\geq0\) and \(y\geq0\) (they can't be negative), so we are only interested in the first quadrant.

To identify the correct graph, we look for a solid line connecting \((12.5,0)\) and \((0,\frac{50}{3})\) with shading in the first quadrant below the line.

Answer:

The graph with a solid line passing through \((12.5,0)\) and \((0,\approx16.67)\) and shading in the first quadrant below the line (the specific graph would be identified based on these intercepts and the inequality conditions, e.g., if there are three graphs, it would be the one matching these criteria).