Question

(b) Antonio compares his plan to another friend, Brielle's. Given that both Antonio and Brielle will only be charged for full minutes, is there an amount of time when their two plans cost the same? Explain. ven that bo Brielle's plan: Monthly cost = 2(1.50m+12)+m-4 where m is the number of minutes used

Answer 1

Antonio's plan is

`3(0.75m+10)+2.50m-15`

Brielle's plan is

`2(1.50m+12)+m-4`

Then, we express both expressions as equivalent to finding the number of minutes needed to cost the same.

`3(0.75m+10)+2.50m-15=2(1.50m+12)+m-4`

First, we use the distributive property.

`2.25m+30+2.50m-15=3m+24+m-4`

Then, we reduce like terms.

`4.75m+15=4m+20`

Then, we subtract 4m on each side.

`\begin{gathered} 4.75m-4m+15=4m-4m+20 \\ 0.75m+15=20 \end{gathered}`

Now, we subtract 15 on each side.

`\begin{gathered} 0.75m+15-15=20-15 \\ 0.75m=5 \end{gathered}`

At last, we divide the equation by 0.75.

`\begin{gathered} (0.75m)/(0.75)=(5)/(0.75) \\ m\approx6.67 \end{gathered}`

This means after 6.67 minutes both plans will cost the same.

This decimal result means that both plans won't be equivalent because only full minutes are charged. In other words, at 6 minutes the plans are not equal.