Question

texting plans
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: x - number of texts, y - total cost (in $). blue line (hiroto) and red line (emilia) intersect at (50, 22.5))

Explanation:

Step1: Analyze the intersection point

The graph shows the intersection point of Hiroto's and Emilia's cost lines at \((50, 22.5)\). This means when \(x = 50\) (number of texts), both plans have a total cost of \(y = 22.5\) dollars.

Step2: Evaluate each option

• Option 1: For more than 50 texts, Emilia's line (steeper) will be above Hiroto's, so Emilia's costs more. This is false.
• Option 2: The intersection is at 50 texts, not 22. This is false.
• Option 3: For more than 50 texts, Emilia's costs more, not 22. This is false.
• Option 4: The intersection \((50, 22.5)\) confirms both cost the same at 50 texts. This is true.

Answer:

D. Both plans cost the same when 50 texts are sent. (Assuming the last option is D; if options are labeled as per the order, the correct one is the last option: "Both plans cost the same when 50 texts are sent.")