9.3.3 Math in Business

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.

total monthly cost in dollar equation left hand side equals right hand side 25 plus open total number of minutes used negative 30 close multiplication 0.2

Activity Symbol 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 Symbol

Answer

As 30 minutes are included in the $25 charge, the number of minutes that are charged separately is 75 minus 30 equals 45.

Each extra minute costs 20¢, so 45 extra minutes will cost 45 postfix multiplication dollar 0.2 equals dollar 9.00.

So, the total charge for that month is dollar 25 postfix plus dollar nine equals dollar 34.00.

The formula says that the fixed charge is $25, and then each minute in excess of the 30 minutes allowed costs 20¢.

Activity Symbol 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 Symbol

Answer

Substituting 48 for the total number of minutes gives the total cost in dollars as:

Total monthly cost in dollar equation left hand side equals right hand side 25 plus open 48 minus 30 close multiplication 0.2
equation left hand side equals right hand side 25 plus 18 multiplication 0.2
equation left hand side equals right hand side 25 plus 3.6
equals 28.6

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

Answer Symbol

Answer

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.

If you have a similar deal you could work out a formula that fits yours and use it to check your bills!

9.3.2 Math in Health Care

9.3.4 Math in Archaeology