For how many minutes will both plans share the same cost?

Question

Talk and text plan a are charged five cents a minute and twenty dollars for 250 texts. Talk and text plan b are charged ten cents a minute(first 100 minutes free) and fifteen dollars for 200 texts. For how many minutes will both plans share the same cost? Show your work algebraically

Answer 1

Plan A talk is 0.05x and text is 8 cents per text.

Plan B talk is 0.10x and text is 7.5 center per text.

For for 1000 texts, plan 8 charges $80 while plan B charges $75

The total cost is 0.05x + 80 = 0.10x +75

0.05x + 5 = 0.10x

5 = 0.05x

500 =5x

x = 100

100 minutes and 1000 texts cost the same amount between both plans, namely

5 + 4 * 20 = 85 = 10 + 5*15