Greenwood press

96
RATES

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The examples described thus far represent rates as values associated with
time. Rates can also be stated in terms of quantities produced or achieved. For
example, the delivery boy receives five cents for each newspaper he drops off
each morning. In addition, Mrs. Newsome’s first-grade class receives twenty
minutes of extra playtime for every one hundred behavior points earned. In a
securities exchange, a rate can be used to illustrate a fair trade, such as in stock
or currency values. For instance, the exchange price of Big Hit Co. today ended
at $48.5 per share. When traveling to Mexico, you would expect to receive an ex-
change rate of about 9.3 pesos for every U.S. dollar.
Rates can also be used to describe changes in an environment or physical set-
ting. For example, two hundred additional employees are needed for every 8 per-
cent increase in demand for the company’s products. In terms of temperature
conversion, there is a change of 1.8° Fahrenheit for every degree Celsius. When
driving along a mountain terrain, a road sign that mentions a 5 percent grade
means that there is a change in elevation of five vertical feet for every one hun-
dred horizontal feet.
Many scientific, engineering, and human measures are rates. Density is a
weight-per-volume measure such as pounds per cubic foot or grams per cubic
centimeter. Sound frequencies, such as those associated with musical notes, are
expressed as rates in cycles per second. Air pressure, such as tire pressure, is
expressed as pounds per square inch. The wealth of countries is compared as the
rate of Gross National Product (GNP) per capita. In 1997, Mexico had GNP per
capita of $8,110; Canada had a GNP per capita of $21,750. States can be com-
pared by population density: the number of people per square mile. Comparisons
may be dramatic. For example, New Jersey has 1,100 people per square mile,
while Wyoming has 4.7.
Comparison shopping requires rates. If an eight-ounce can of corn sells for
98 cents, the unit cost is 98/8 = 12.25 cents per ounce. A ten-ounce can that sells
for $1.02 would have a unit cost of 102/10 = 10.20 cents per ounce. The larger
can is the better deal, because it provides the lower unit cost.
Rate, in mathematics courses through algebra, is often presented as having a
constant value. When you read about the speed of an object or a person’s work
wages, it is assumed that there will not be any change in these values. In such
cases, the rate can be represented as the slope of a linear function that describes
a total amount. For example, if you are earning $8 per hour for delivering pizzas,
and always earn wages at that rate, then your total earnings, 
e, in terms of the
number of hours you have worked, 
h, can be represented by the equation e = 8h.
Notice that the hourly rate is the same as the slope of the linear function. 
Suppose you wanted to make copies for a class presentation at the local copy
shop. If the machine charges 10 cents per copy, then the total amount of money,
m, that you would need would depend on the number of copies, c, you make.
Since 0.10 is the rate in dollars, the equation 
m = 0.10c would help you deter-
mine the amount of money you would need, or the number of copies you could
make with a certain amount of money. For example, if you had $4.30 in your