# Thread: Mobile Phone rate plans - HELP!

1. ## Mobile Phone rate plans - HELP!

Imagine.. A $50 mobile phone plan. Mobile calls 10c per 30 seconds. Land Line calls 29c per 30 seconds. A customer states "30% of my calls are to mobiles, the other 70% are to landlines, how many hours of talk time (in decimal) do I get for mobile calls and landline calls?" I need an equation for this to which I could apply if the percentages changed to say 15% and 85%. Thanks guys Psylencer. By the way I need a response I can understand...Im no maths genius. Thanks 2. Hello, psylencer! Not to worry . . . Baby-talk is my specialty. Imagine.. A$50 mobile phone plan.

Mobile calls: 10¢ per 30 seconds.
Land Line calls: 29¢ per 30 seconds.

A customer states "30% of my calls are to mobiles, the other 70% are to landlines.
How many hours of talk time (in decimal) do I get for mobile calls and landline calls?"

I need an equation for this to which I could apply if the percentages changed to, say, 15% and 85%.

Let's solve this particular problem first . . . then we'll generalize it.

Let $\displaystyle T$ = total talk time (in hours).

The rates are: $\displaystyle \begin{array}{cc}\text{Mobile: \$12/hour} \\ \text{Land: \$34.80/hour}\end{array}$

Since 30% of the calls are Mobile, he talks $\displaystyle 0.3T$ hours at $12/hour. . . His mobile calls cost him:$\displaystyle (0.3T)(12) = 3.6T$dollars. Since 70% of the calls are Landline, he talks$\displaystyle 0.7T$hours at$38.40/hour.
. . His landline calls cost him: $\displaystyle (0.7T)(38.40) = 24.36T$ dollars.

His total cost will be $50: .$\displaystyle 3.6T + 24.36T\;=\:50$Solve for$\displaystyle T:\;\;27.96T = 50\quad\Rightarrow\quad\boxed{T = 1.788268956\text{ hours.}}$For his$50, he can talk a total of: $\displaystyle \text{1 hour, 47 minutes, 17 seconds}$

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Now, we'll generalize the problem,
. . keeping the hourly rates constant.

Let $\displaystyle p$ = percent of T used on Mobile calls.
. . Time on mobile calls: $\displaystyle pT$ hours.
Then mobile calls cost: $\displaystyle pT \times 12 = 12pT$ dollars.

Then $\displaystyle 1 - p$ = percent of T used on Landline calls.
. . Time on landline calls: $\displaystyle (1-p)T$ hours.
Then landline calls cost: $\displaystyle (1-p)T \times 38.4 = 38.4T - 38.4pT$ dollars.

The total cost is $50, so: .$\displaystyle 12pT + (38.4T - 38.4pT) \:=\:50$Solve for$\displaystyle T$and we get: .$\displaystyle \boxed{T \:= \:\frac{50}{34.8 - 22.8p}\text{ hours.}}\$

3. Thanks Soroban,

I got the first part, but not the last part. As you can probably tell, Im interested in maths (not a student) but no good at it. Any chance we could go back a step? I still dont see how the percentages work. HOLD ON!...I GOT IT..HAHA! Dont worry Thanks heaps. You guys are brilliant.

Thanks
Psylencer