One of the advantages of identifying the general features of a calculation and then describing it mathematically is that the formula can then be used in either a computer or a calculator program to work out different calculations quickly and efficiently. Many utility suppliers (gas, water, electricity, telephone) have rates based on a fixed daily (or monthly or quarterly) charge and a further charge based on how much you have used during the billing period.

For example, in 2005, a mobile phone network charged $25 per month for 30 minutes (or less) of phone calls. Extra calls above the 30 minutes were charged at 20¢ per minute. Assuming that more than 30 minutes were used per month, the formula for the total monthly cost can be expressed by the following word formula. ## Activity: Understanding the Formula Suppose that in one month, 75 minutes of phone calls were made. Explain how you would calculate the cost for the extra minutes (above the 30-minute allowance) and then how to calculate the total cost for that month. Can you explain how the formula has been derived? ### Answer As 30 minutes are included in the$25 charge, the number of minutes that are charged separately is .

Each extra minute costs 20¢, so 45 extra minutes will cost .

So, the total charge for that month is .

The formula says that the fixed charge is $25, and then each minute in excess of the 30 minutes allowed costs 20¢. ## Activity: Phone Bills On this phone bill, what would the monthly charge have been if the total time for the calls were the following? (a) 48 minutes ### Answer Substituting 48 for the total number of minutes gives the total cost in dollars as: So, the bill for the month is$28.60.

Note how this calculation is set out with a concluding sentence that answers the question precisely.

(b) 25 minutes

The formula only applies if more than 30 minutes of calls are made, so it cannot be used in this case. This is an important step in using formulas—check that they apply in your situation before using them. Here, the charge is $25 for up to 30 minutes of calls, so the charge for this month is$25 overall.