Luis wants to change companies for his phone service. Company SaveMore charges $16 for the initial service plus $0.20 for every 1 text of use.Write an equation that represents the cost of the service, with the cost of the constant number of text, t added After how many texts will the two companies be the same charge for the service?

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MrRoyal MrRoyal · Answer 1 · 2021-06-22T21:09:43+02:00

Answer:

[tex]y = 16 + 0.2t[/tex] --- the equation of SaveMore company

Step-by-step explanation:

Given

SaveMore

[tex]Initial = 16[/tex]

[tex]Additional\ Rate = 0.20[/tex]

Required

Determine the equation

Let

[tex]y \to cost[/tex]

[tex]t \to texts[/tex]

So, we have:

[tex]y = Initial + Additional\ Rate * t[/tex]

[tex]y = 16 + 0.20 * t[/tex]

[tex]y = 16 + 0.2t[/tex]

The equation for the second company is not given. So, the (b) part cannot be correctly answered.

A general solution to the (b) part is:

Assume the equation is:

[tex]y = 10 + 0.4t[/tex]

Next, we equate both

i.e.

[tex]y = y[/tex]

This gives:

[tex]16 + 0.2t = 10 + 0.4t[/tex]

Collect like terms

[tex]0.4t - 0.2t = 16 - 10[/tex]

[tex]0.2t = 6[/tex]

Divide by 0.2

[tex]t = 30[/tex]

Hence, the charges will be the same after 30 texts