Question

hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. emilia’s plan costs $10 per month and $0.25 per text. using the graph below, which statement is true?
○ hiroto’s plan costs more than emilia’s plan when more than 50 texts are sent
○ both plans cost the same when 22 texts are sent
○ emilia’s plan costs more than hiroto’s plan when more than 22 texts are sent
○ both plans cost the same when 50 texts are sent.
(graph: title: texting plans, x-axis: number of texts (10,20,30,40,50,60,70,80,90,100), y-axis: total cost (in $) (3,6,9,12,15,18,21,24,27), two lines: emilia (red, starts at (0,9), passes through (50,22.5)) and hiroto (blue, starts at (0,20), passes through (50,22.5)) )

Explanation:

Step1: Analyze the graph's intersection point

The graph shows the total cost (y - axis) vs. number of texts (x - axis). The intersection point is \((50, 22.5)\), meaning at \(x = 50\) texts, both plans have a total cost of \(y=\$22.5\).

Step2: Evaluate each option

• Option 1: For \(x>50\), Emilia's line (red) is above Hiroto's (blue), so Emilia's costs more. False.
• Option 2: The intersection is at \((50, 22.5)\), not 22 texts. False.
• Option 3: For \(x > 50\) (not 22), Emilia's costs more. False.
• Option 4: The intersection point \((50, 22.5)\) means at 50 texts, both costs are equal. True.

Answer:

D. Both plans cost the same when 50 texts are sent.