## lizz123 one year ago Medal One cell phone plan charges 20 dollars per month plus 0.15 cents per minute used. A second cell phone plan charges 35 dollars per month plus 0.10 cents per minute used. Find the number of minutes you must talk to have the same cost for both calling plans.

1. Michele_Laino

the cost for the first phone is: ${c_1} = 20 + 0.15 \times m$ where m is the number of minutes. Whereas the cost for the second phone is: ${c_2} = 35 + 0.10 \times m$

2. Michele_Laino

now we have to know the number m of minute

3. Michele_Laino

minutes*

4. lizz123

$c _{1}=20+.15\times1$ 20.15

5. lizz123

c1=20+.15*2 20.30

6. Michele_Laino

yes! nevertheless we have to find the value of m. In order to that we see that the cost c_1 is equal to the cost c_2 when the subsequent equation holds: $\begin{gathered} {c_1} = {c_2} \hfill \\ 20 + 0.15 \times m = 35 + 0.10 \times m \hfill \\ \end{gathered}$

7. Michele_Laino

please solve that equation for m

8. lizz123

Can I do a chart

9. Michele_Laino

if you want you can do a chart. We can get the answer if we solve that equation for m

10. Michele_Laino

$\Large 20 + 0.15 \times m = 35 + 0.10 \times m$

11. lizz123

C1=20+0.15*3= 20.45 C2=20+0.10*3= 20.330

12. lizz123

I mean 20.30

13. lizz123

So I have to find the same answer for the same time of minutes

14. Michele_Laino

ok! Please substitute m=100, what do you get?

15. lizz123

$\huge c _{1}=20+.15 * 100 = 35$

16. Michele_Laino

and c_2?

17. lizz123

$\huge c _{2}= 35 +.10 * 100=45$

18. Michele_Laino

ok! So they are different again. I think that the solution is m=300. Am I right?

19. lizz123

$\huge c _{1}= 20 + .15*300= 65$ $\huge c _{2}=35+.10*300=65$ Yes, m does equal 300.

20. Michele_Laino

perfect! So you can do your chart, using the subsequent values for m: 1, 20, 50, 100, 300 for example

21. lizz123

okay thanks

22. Michele_Laino

:)