I need help With this question

Question

Molly is supposed to call her friend every Thursday night. Sometimes they have a lot to talk about, other times not so much. There are two phone companies she can use: TCC charges $0.10 per minute (no matter how long the call). UFC charges $0.50 for the first minute plus $0.08 for every minute thereafter. How many minutes can Molly talk to be charged the same amount by either phone company? this is my work and you can see that it they are both are same at 21 but when I do it as an equation I get 25

        TCC       UFC

1. 0.10      0.50
2. 0.20      0.58
3. 0.30      0.66
4. 0.40      0.74
5. 0.50      0.82
6. 0.60      0.90
7. 0.70      0.98
8. 0.80      1.06
9. 0.90      1.14
10. 1.00      1.22
11. 1.10      1.30
12. 1.20      1.38
13. 1.30      1.46
14. 1.40      1.56
15. 1.50      1.62
16. 1.60      1.70
17. 1.70      1.78
18. 1.80      1.86
19. 1.90      1.94
20. 2.00      2.02
21. 2.10      2.10

 

Answer 1

Considering the common multiples of .08 and .10, every iteration of 5 and 10 minutes after the first minute are the only possibilities for the two to be equal. Now we know that TCC = .10m and UCC = .50(m₁) + .08(m_n-m₁). The formula should be:

.10m = .50 + .08(m-1)....

Expanding out is .10m = .50 + .08m - .08.....

simplifying --> .02m = .42....

now dividing both sides by .02 -->m=21