# 7 Formulas

You may use a calculator throughout this module if needed.

A formula is an equation or set of calculations that takes a number (or numbers) as input, and produces an output. The output is often a number, but it could also be a decision such as yes or no.

Each unknown number in a formula is called a variable because its value can vary. A variable is usually represented with a letter of the alphabet. To evaluate a formula, we substitute a number (or numbers) into the formula and then perform the steps using the order of operations.

# Formulas with One Input

Many formulas will have just one input variable. Note: When a number is written directly next to a variable, it indicates multiplication. For example, means .

Exercises

The formula gives the cost, in dollars, of mailing a large envelope weighing ounces through the USPS.^{[1]}

- Find the cost of mailing a -ounce envelope.
- Find the cost of mailing a -ounce envelope.

Radio Cab charges the following rates for a taxi ride: a fixed fee of to get in the taxi, plus a rate of per mile.^{[2]} The total cost, in dollars, of a ride miles long can be represented by the formula .

- Find the cost of a -mile ride.
- Find the cost of a -mile ride.
- Find the cost of getting in the taxi, then changing your mind and getting out without riding anywhere.

The number of members a state has in the U.S. House of Representatives can be approximated by the formula , where is the population in millions.^{[3]} The 2020 populations of three states are as follows:^{[4]}

Oregon | |

Washington | |

California |

Round all answers to the nearest whole number.

- How many U.S. Representatives does Oregon have?
- How many U.S. Representatives does Washington have?
- How many U.S. Representatives does California have?

The number of electoral votes a state has can be approximated by the formula , where is the population in millions.

- How many electoral votes does Oregon have?
- How many electoral votes does Washington have?
- How many electoral votes does California have?

# Temperature Conversions

You probably know that ° Fahrenheit is the freezing point of water, and ° Fahrenheit is the boiling point of water. The Celsius equivalents are °C and °C. The formulas shown below allow us to convert between the two temperature scales.

**Temperature Formulas**

Exercises

- The record high temperature in Portland, Oregon occurred during the “heat dome” event in June, 2021. As shown, it was °C at your author’s house and the squirrels were laying low. Convert this temperature to Fahrenheit.

- The traditionally accepted “normal” body temperature of a human
^{[5]}is °F. What is this temperature in Celsius? - The FDA recommends that a freezer be set below °C. What is the Fahrenheit equivalent?
- A package of frozen pancakes from IKEA calls for the oven to be set to °F. IKEA is based in Sweden, and this temperature clearly was originally calculated in Celsius. What is the corresponding Celsius temperature?

# Formulas with More than One Input

Some formulas have more than one input variable. Just pay attention to which number goes in for each variable.

Exercises

When a patient’s blood pressure is checked, they are usually told two numbers: the systolic blood pressure (SBP) and the diastolic blood pressure (DBP). The mean arterial pressure (MAP) can be estimated by the following formula: . (The units are mm Hg.) Calculate the mean arterial pressure for each patient.

- SBP = , DBP =
- SBP = , DBP =

UPS uses the following formula^{[6]} to determine the “measurement” of a package with length , width , and height : . Determine the measurement of a package with the following dimensions.

- length inches, width inches, height inches
- length inches, width inches, height inches

# Formulas with a Yes or No Answer

Some formulas give a yes or no answer: success or failure, approved or disapproved, etc. After calculating the result from the formula, we need to compare it to a given number to see whether the result is within a specified range.

Exercises

In Australia, a chicken egg is designated “large” if its mass, in grams, satisfies the following formula: . Determine whether each egg qualifies as large.^{[7]}

- Egg 1’s mass is grams.
- Egg 2’s mass is grams.
- Egg 3’s mass is grams.
- Egg 4’s mass is grams.

- Source: https://pe.usps.com/text/dmm300/Notice123.htm#_c037 ↵
- Source: https://www.radiocab.net/services-radio-cab/ ↵
- The value 0.76 comes from dividing the total U.S. population in 2020, around 331 million people, by the 435 seats in the House of Representatives. ↵
- Source: https://www.census.gov/data/tables/2020/dec/2020-apportionment-data.html ↵
- See this article for a counterargument: https://www.nytimes.com/2023/10/12/well/live/fever-normal-body-temperature.html ↵
- Source: https://www.ups.com/us/en/help-center/packaging-and-supplies/prepare-overize.page ↵
- Source: https://en.wikipedia.org/wiki/Chicken_egg_sizes ↵

an unknown value that is usually represented by a letter