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.

Answer 1

The true statement is: "Both plans cost the same when 50 texts are sent."

Reason: Let n be the number of texts. Hiroto: 20 + 0.05n. Emilia: 10 + 0.25n. Set equal:
20 + 0.05n = 10 + 0.25n → 10 = 0.20n → n = 50. For n > 50 Emilia becomes more expensive.