Algebra 1
Unit Activity
Answer Sheet
Unit: Relationships Between Quantities and Reasoning with
Equations
This Unit Activity will help you meet these educational goals:
 Mathematical Practices—You will make sense of problems and solve them, use
mathematics to model real-world situations, and use appropriate tools strategically.
 Inquiry—You will conduct online research in which you will collect information and
communicate results in tables, graphs, and written form.
Introduction
Have you ever made a mistake when trying to solve a math problem? It can be pretty easy to
do, and often will result in losing points on an exam. In the real world, such mistakes can
have more serious effects: Miscalculating how much gas you have left in your car will leave
you stranded. Miscalculating how much money you have left in your bank account might cost
you an overdraft fee. Even more serious, miscalculations have resulted in serious accidents
happening many times. Once, as a result of not using the correct units, a satellite sent to
Mars burned up in the atmosphere, wasting over $300 million dollars.
Fortunately, there are steps you can take to help avoid making errors along the way. One of
these strategies is manipulating formulas so they are solving for the variable you want before
you substitute values for the variables in the formula. This technique is especially useful
when working with large, unwieldy numbers.
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Directions and Analysis
Task 1: A Journey to Earth
Every moment of every day, light pours out from the Sun at the center of our solar system
and travels to Earth. It does not arrive at Earth instantaneously though; it takes time to get
here. Your task is to figure out how long it takes for light to travel from the Sun to Earth.
d
, where v is the velocity of the object, d is
t
the distance traveled, and t is the time elapsed while that distance is traveled. If you had
only this formula to work with, what should your first step be in determining how long it
takes for light to reach Earth from the Sun? What additional information do you need to
calculate this?
a. The formula for the velocity of an object is v 
Sample answer:
To solve for the time it takes for light to reach Earth from the Sun, you need to solve for t.
The additional information needed is the distance between the Sun and Earth, as well as
the velocity the light travels at.
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b. Solve for the variable you are looking for. Show your work.
Sample answer:
d
v
t
t
d t
v  
v
t v
d
t
v
c. Now search the Internet for the values of the variables you do not know. What are they?
Sample answer:
The velocity of light is 299,792,458 meters per second. The distance between Earth and
the Sun is 1 astronomical unit, or 149,597,870,700 meters.
d. Using the formula you derived and the values you researched, calculate the time it takes
for light to travel from the Sun to Earth.
Sample answer:
d
t
v
149,597,870,700 meters
t
299,792,458 meters per second
t = 499 seconds, or about 8.3 minutes
e. Felix Baumgartner is a daredevil famous for breaking the sound barrier during a freefall on
October 14, 2012. Aided by a weather balloon, he climbed to a height of 128,100 feet.
More than 24 miles in the air, he was so high up that he could see Earth’s curvature. He
then jumped out of the capsule that carried him. On the way down, he traveled at an
average of 335.92 miles per hour, at one point even going as fast as 720 miles per hour,
breaking the record for the highest skydive ever attempted and breaking the sound barrier
in the process. Using the formula you derived in part b, how long did it take Baumgartner
to reach the ground, in minutes? Be careful about unit conversions, and show your work.
Sample answer:
First convert the units so they are in the appropriate form. The height is in feet and the
velocity is given in miles per hour, so convert to feet per hour:
d (feet)
1 mile
t

.
 miles  5,280 feet
v

 hour 
Next, convert hours to minutes:
2
t
d (feet)
1 mile
60 minutes


.
1 hour
 miles  5,280 feet
v

 hour 
Now insert the values and simplify:
128,000 feet
1 mile
60 minutes
t


 4.22 minutes
335.92 miles / hour 5,280 feet
1 hour
Task 2: Interest in Finance
Interest is a concept familiar to most people: every credit card in existence has a term called
annual percentage rate (APR), which is an interest rate. Suppose you charged $1,000 to a
credit card that has a minimum payment each month equal to the interest owed. Can you
figure out how much the interest rate is based on this amount?
The formula for simple interest is I  r  P  m, where I is the amount you will pay in interest, r
is the rate at which interest will accrue, P is the principal (amount borrowed), and m is the
number of times the interest is applied.
a. To solve for the interest rate of your credit card, you need to understand which variables
in the above formula you have. If your minimum monthly payment is $22 on the $1,000
credit card bill, which variables do you know the values of?
Sample answer:
You know the values of I, P, and m. Only r is unknown.
b. Manipulate the formula so it will calculate the interest rate you are paying instead of the
amount of money you are paying.
Sample answer:
I
r
P m
c. Now that you have a formula that will give you the interest rate, plug in the values for the
problem and solve for that interest rate. Interest rates are usually represented for a time
period: over what time period does this rate apply? What would the interest rate be if it
were a yearly rate?
Sample answer:
The interest rate is 2.2%. This is the amount of interest accrued in a single month. If it
were a yearly rate, the interest rate would be 26.4%.
d. Now consider a different situation. Payday loans are a type of loan where you can get
money for a future paycheck, typically two weeks in advance. A typical payday loan
service might charge $15 for a loan against a paycheck you will receive in two weeks. The
interest rate is 10% of the paycheck over that two-week period. Given this information,
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which variables in the interest formula are known? Develop a formula that will solve for
the unknown variable.
Sample answer:
The unknown variable is P, which is the amount borrowed—in this case, the amount of
I
the paycheck. Solving the interest formula for P gives the formula
 P.
r m
e. Solve for the value of the unknown variable.
Sample answer:
The paycheck (P) is $150.
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Resources
Document any references you used for this project below. At minimum, include a title and
URL for any Internet resource:
__________________________________________________________________________
Evaluation
This project will be evaluated on a rubric that is based on the completeness, clarity, and
thinking you exhibit in the Directions and Analysis section above.
Total Points: 10
Task 1: A Journey to Earth
a. Identifying known variables
Task points: 5
 1
b. Manipulating the formula to solve for the desired variable

1
c. Researching for variable amounts

1
d. Calculating time to reach Earth

1
e. Applying formula to a daredevil’s fall

1
Task 2: Interest in Finance
a. Identifying known variables
Task points: 5
 1
b. Manipulating the formula to solve for the desired variable

1
c. Determining yearly interest rate

1
d. Manipulating the formula for a new situation

1
e. Calculating a paycheck based on a payday loan interest
rate and interest amount

1
4