Cell phone problem

Question

Enrique has a pay per use plan on his cell phone. It costs $0.10 per minute talk, $.20 per text message, and $.25 per picture message. His total bill last month was $30.95. The total number of text and picture messages sent was 87. The cost for the use of minutes was $ 1.60 less than the cost of the text messages. Find the number of talk minutes, text messages, and picture messages he used.

Answer 1

Hi Stac;

 

Cost as a function of # minutes, texts, pictures:

c(m,t,p) = 0.1m + 0.2t + 0.25p

 

Total cost for the month is $30.95:

0.1m + 0.2t + 0.25p = 30.95  

multiply through by 100

10m + 20t + 25p = 3095      {equation 1}

 

total number of text and picture messages sent was 87:

t + p = 87  {equation 2}

 

minutes was $1.60 less than the cost of the text messages

0.1m = 0.2t - 1.6 

multiply through by 10

m = 2t - 16     {equation 3}

 

Using equation 2, solve for t in terms of p

t = 87 - p

 

From equation 3:

m = 2(87-p) - 16

m = 174 - 2p - 16

m = 158 - 2p

 

We now have both t and m in terms of p

Plugging that information into equation 1:

10m + 20t + 25p = 3095

 

10(158-2p) + 20(87-p) + 25p = 3095

1580 - 20p + 1740 - 20p + 25p = 3095

3320 -15p = 3095

-15p = -225

p = 15 picture texts

 

m = 158-2p = 158 - 30 = 128 minutes used or 2 hours 8 minutes

 

t = 87 - p = 87 - 15 = 72 texts sent

 

I'll leave it to you to plug the answer into the original equations

and verify they balance.