AlgebraApplications of Equation Solving

Unit Two: Assignment #5

Equation Solving: Formulas

  1. The following formula relates the temperature in degrees Fahrenheit to the temperature in degrees Celsius:

The variables in this formula are defined as follows:

F = Temperature in degrees Fahrenheit

C = Temperature in degrees Celsius

If the temperature is 75 degrees Fahrenheit, what is the temperature in degrees Celsius?

  1. The following formula describes the total distance required to stop a car after a driver receives a visual stimulus such as seeing the break lights of a car or seeing something jump into the road.

The variables in this formula are defined as follows:

D = the estimated total stopping distance

r = the car’s speed in miles per hour

F = the driving surface factor

T = the reaction time of the driver in seconds

If a car is traveling at a speed of 60 mph and a deer jumps out into the road 250 away, what does the driver’s reaction time of the driver need to be in order for him to stop the car in time? Assume that the car is traveling on a wet asphalt road, which has a driving surface factor of .65.

  1. A baseball player’s batting average is found by using the following formula:

The variables in this formula are defined as follows:

B = Batting Average (decimal rounded to the nearest thousandth)

H = # of hits

A = # of at bats

  1. Roger has 120 hits in 400 at-bats so far this year. What is his current batting average?
  2. Roger expects to get 150 more at bats this year. How many more hits will he need in order to end with a batting average of .310?
  1. The following formula describes the length of a belt needed to connect two pulleys on a machine.

L= 3.14(.5D + .5d) + 2x

The variables in this formula are defined as follows:

L = belt length

D = the diameter of the bigger pulley

d = the diameter of the smaller pulley

x = the distance between the center of the pulleys

A larger pulley with a diameter of 6.25 inches is to be connected to a smaller pulley by a belt that is 56 inches long. The centers of the two pulleys need to be exactly 20 inches apart. What does the diameter of the smaller pulley need to be?

Equation Solving: Situations Involving “Per”

For each of the following word problems, complete the following four steps:

1. Define a variable

2. Write an equation.

3. Solve the equation.

4. Answer the question in a complete sentence.

  1. The bill (parts and labor) for the repair of a car was $458. The cost of parts was $339. The cost of labor was $34 per hour. How many hours of labor were spent on repairing the car?
  1. Your school’s drama club charges $4 per student for admission to Our Town. The club borrowed $400 from parents to pay for costumes, props, and the set. After paying back the parents, the drama club has $100. How many students attended the play?
  1. You earn $9 per hour. On major holidays, such as Thanksgiving, you earn twice as much per hour. You earned a total of $405 for the week including Thanksgiving. How many hours did you work on Thanksgiving if you worked 35 hours during the rest of the week?
  1. A local computer center charges nonmembers $5 per session to use the media center. If you pay a membership fee of $25, you pay only $3 per session. How many times must you use the media center to justify becoming a member?
  1. A rock-climbing gym charges nonmembers $16 per day to use the gym and $8 per day for equipment rental. Members pay a yearly fee of $450 for unlimited climbing and $6 per day for equipment rental. How many times must you use the gym to justify becoming a member?
  1. At BartonHigh School, 45 students are taking Japanese. This number has been increasing at a rate of 3 students per year. The number of students taking German is 108 and has been decreasing at a rate of 4 students per year. At these rates, when will the number of students taking Japanese equal the number taking German?
  1. A bottle-nosed dolphin can dive 440 feet per minute. Suppose a bottle-nosed dolphin is 500 feet deep and dives at this rate. How long will it take for the dolphin to reach a depth of 2975 feet?
  1. Your school band is planning to attend a competition. The total cost for the fifty band members to attend is $750. Each band member will pay $3 toward this cost and the rest of the money will be raised by selling wrapping paper. For each roll of wrapping paper sold, the band makes $2. How many rolls will the band members need to sell in order to cover the cost of attending the competition?