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 manyhoursof 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 = total talk time (in hours).

The rates are:

Since 30% of the calls are Mobile, he talks hours at $12/hour.

. . His mobile calls cost him: dollars.

Since 70% of the calls are Landline, he talks hours at $38.40/hour.

. . His landline calls cost him: dollars.

His total cost will be $50: .

Solve for

For his $50, he can talk a total of:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Now, we'll generalize the problem,

. . keeping the hourly rates constant.

Let = percent of T used on Mobile calls.

. . Time on mobile calls: hours.

Then mobile calls cost: dollars.

Then = percent of T used on Landline calls.

. . Time on landline calls: hours.

Then landline calls cost: dollars.

The total cost is $50, so: .

Solve for and we get: .