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# Formulas and Mixtures Word Problems Study Guide (page 2)

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Updated on Aug 24, 2011

#### Example

Kimberly hears that the temperature in Sydney, Australia, is 22° Celsius. What is the temperature in Sydney in degrees Fahrenheit?

We are given a temperature in degrees Celsius.

We are looking for a temperature in degrees Fahrenheit.

Underline the keywords and words that indicate formulas.

The words Celsius and Fahrenheit tell us that we need to use a temperature conversion formula.

Cross out extra information and translate words into numbers.

There is no extra information in this problem.

List the possible operations.

We will use multiplication and addition to convert from degrees Celsius to degrees Fahrenheit.

Write number sentences for each operation.

Substitute the temperature in degrees Celsius into the formula:

F = (22) + 32

Solve the number sentences and decide which answer is reasonable.

F = (22) + 32 = 39.6 + 32 = 71.6°

We can use the formula for converting Fahrenheit to Celsius to check our answer. C = (F – 32) = (71.6 – 32) = (39.6) = 22° Celsius

#### Inside Track

When taking final exams and state tests, often you are given a limited amount of time to finish the exam. You may find that using the eight-step process for every word problem takes a little too much time. If you can recognize a formula word problem after studying the keywords and reading the question carefully, you can skip the eight-step process and plug the given numbers right into the formula. The eight-step process can always help you find what operations or formulas to use, and it reminds you to check your work. It's the best way to go, but if you are pressed for time, it may be faster to use a formula.

#### Example

Dianne's pencil is 176 millimeters long. How long is her pencil in meters?

Let's say we need to work quickly and do not have time for the eight-step process. This problem is asking us to convert millimeters to meters. To convert from millimeters to meters, we must divide the number of millimeters by 1,000: = 0.176 meters. Dianne's pencil is 0.176 meters long.

#### Example

Dianne earns \$228 in interest on \$1,500 that she kept in a bank for four years. What was the interest rate on Dianne's principal?

We know that I = prt, so to solve for r, the interest rate, we must rearrange the equation. If we divide both sides of the equation by p and t, we have r = . Substitute the interest, principal, and time into the formula to find the interest rate: = 0.038 = 3.8%.

#### Caution

Read the units of each value in a word problem carefully. If a distance problem gives you a rate in meters per second and a time in seconds, you are ready to multiply, but if the rate is given in meters per second and the time is given in minutes, you must either convert the rate to meters per minutes or convert the time to seconds before multiplying. In the same way, if you are looking to find interest earned, the rate and time must also be given in the same units. You may need to convert one number from months to years.

#### Example

Fernando throws a baseball at a speed of 90 miles per hour. How many seconds does it take the ball to travel 60.5 feet?

We are given a rate and a distance, and we are looking for a time. However, our rate is given in miles per hour and our distance is given in feet. We must either convert our rate to feet per hour or convert the distance to miles. Since there are 5,280 feet in a mile, 60.5 feet is equal to , or approximately 0.0116 miles. The distance formula is D = rt, but we are looking for t, the time. Divide both sides of the equation by r, and t = , which equals 0.000129. Our rate was given in miles per hour, so this is the number of hours it takes the ball to travel 60.5 feet. There are 60 minutes in an hour and 60 seconds in a minute, which means that we must multiply the time in hours by 60 × 60 = 3,600. So, 0.000129 × 3,600 = 0.4644 seconds.

#### Pace Yourself

Use a map to find how far you live from your school. Use the time it takes you to walk to school to find your average rate of speed, in miles per hour. If you take a car or bus to school, use that time to find the average rate of speed in miles per hour of the car or bus.

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