3.4 Manipulating Equations

Last updated about 1 year ago

31 questions

Note from the author:

OBJECTIVES & STANDARDS
Math Objectives
Solve literal equations for a given variable
Convert linear equations from standard form to slope-intercept form
Common Core Math Standards
Link to all CCSS Math
CCSS.PRACTICE.MP2
CCSS.HSA.SSE.B.3
CCSS.HSF.BF.A.1
Personal Finance Objectives
Explore simple interest and savings accounts
National Standards for Personal Financial Education
Saving
2a: Select a preferred location for a savings account based on comparison of interest rates and fees at different types of financial institutions
DISTRIBUTION & PLANNING
Distribute to students
Student Activity Packet
Application Problems

Instructions

OBJECTIVES & STANDARDS
Math Objectives
Solve literal equations for a given variable
Convert linear equations from standard form to slope-intercept form
Common Core Math Standards
Link to all CCSS Math
CCSS.PRACTICE.MP2
CCSS.HSA.SSE.B.3
CCSS.HSF.BF.A.1
Personal Finance Objectives
Explore simple interest and savings accounts
National Standards for Personal Financial Education
Saving
2a: Select a preferred location for a savings account based on comparison of interest rates and fees at different types of financial institutions
DISTRIBUTION & PLANNING
Distribute to students
Student Activity Packet
Application Problems

Intro - Warm-Up

Learn It

Application Problems

Level 2

3.4 Manipulating Equations

Last updated about 1 year ago

31 questions

Note from the author:

OBJECTIVES & STANDARDS
Math Objectives
Solve literal equations for a given variable
Convert linear equations from standard form to slope-intercept form
Common Core Math Standards
Link to all CCSS Math
CCSS.PRACTICE.MP2
CCSS.HSA.SSE.B.3
CCSS.HSF.BF.A.1
Personal Finance Objectives
Explore simple interest and savings accounts
National Standards for Personal Financial Education
Saving
2a: Select a preferred location for a savings account based on comparison of interest rates and fees at different types of financial institutions
DISTRIBUTION & PLANNING
Distribute to students
Student Activity Packet
Application Problems

Instructions

OBJECTIVES & STANDARDS
Math Objectives
Solve literal equations for a given variable
Convert linear equations from standard form to slope-intercept form
Common Core Math Standards
Link to all CCSS Math
CCSS.PRACTICE.MP2
CCSS.HSA.SSE.B.3
CCSS.HSF.BF.A.1
Personal Finance Objectives
Explore simple interest and savings accounts
National Standards for Personal Financial Education
Saving
2a: Select a preferred location for a savings account based on comparison of interest rates and fees at different types of financial institutions
DISTRIBUTION & PLANNING
Distribute to students
Student Activity Packet
Application Problems

Intro - Warm-Up

CALCULATE: Solving equations
Solve each of the following equations for x.
SHOW YOUR WORK FOR FULL CREDIT

-2x + 11 = 15
x=_______ 

6x + 4 = -3x - 5
x=_______ 

Learn It

Solving Literal Equations
Let’s solve some more equations, except this time, we’re going to write down what steps we’re doing and why we’re doing them.
In the “Equation” column, write the equation solving steps.
In the “Description and Reason” column, write a short word description of what you did and why you did it.  For example, “I subtracted by 5 on both sides of the equation to get the 2x by itself.” *Use the Properties of Equality*

Solve the Equation for x: 
Equation               Reason
1.  4x+5=25        1.  Given
2. 4x=_______   2. _______ Prop. of =
3.  x=_______    3.  _______ Prop of =

Solve the equation for b: 
Equation               Reason
1.  ab+c=d       1.  Given
2. ab=_______  2. _______ Prop. of =
3.  _______     3.  _______ Prop of =

Notice how the steps for these two problems are identical!  The only difference is that when numbers are included, you can simplify as you go and when there are only variables, you can’t.  These equations that contain mostly variables are called literal equations.

Notice how the steps for these two problems are identical!  The only difference is that when numbers are included, you can simplify as you go and when there are only variables, you can’t.  These equations that contain mostly variables are called literal equations.

Here are some basic steps you can follow to solve any equation for a given variable.
Review the completed example problem, using the video walkthrough.
1
Find and Combine:
Find the term with your variable. Combine like terms if necessary.
Solve for y:

zx+by=r

2
Isolate the term:
Add or subtract all other terms to isolate the term containing your variable.
zx - zx + by = r - zx
by = r - zx

3
Isolate the variable:
Multiply or divide away anything that is connected to your variable. Be sure to apply your operation to ALL terms on both sides




4
Check your Answer:
Your variable should be the only term on that side of the equation

Application Problems

Simple Interest
Interest is the amount of money that someone is paid for allowing someone else to borrow their money.  If you take out a loan on a car, you may have to pay interest to borrow the money you need to make the car purchase.  Similarly, if you put money into a savings account, you can EARN interest.
There are many different ways of calculating interest.  We are going to be focusing on simple interest, where only your initial deposit earns interest.  Simple interest is calculated using the following formula:

Where
I = Total Interest
P = Principal (the amount that is being borrowed or deposited)
r = the annual interest rate as a percent (APR)
t = the number of years

Level 2

Savings Account Interest
You invest a total of $12,000 in two savings accounts paying 0.61% and 0.70% simple annual interest. If the yearly interest is $75, how much of the $12,000 did you deposit into each account?
Review:  To convert a percent into a decimal, move the decimal point two places to the left.  For example, 3% becomes 0.03.

Write a system of equations that represents this situation.
a.  Focus on the question at the end of the situation. What is unknown?  Define variables to represent these unknowns.
x=_______ y=_______ 
b.  What are the TWO situations that are being described in the problem?  Write an equation that represents each situation._______ _______ 

Where do these lines intersect?
Enter both equations from Part 1 into the Desmos Graphing Calculator and write down the intersection point.  You may need to zoom out to find the intersection._______ 

Calculate the interest rates
You deposit $10000 into a standard simple interest savings account.  You deposit $12000 into a higher yield account whose interest rate is triple the basic account.  In one year, you make $460 in interest.  What were the interest rates for each account?
Part I
Write a system of equations that represents this situation where x represents the standard savings account and y represents the high yield savings account.
Focus on the question at the end of the situation. What is unknown about the situation?  Define variables to represent these unknowns.
What are the TWO situations that are being described in the problem?  Write an equation that represents each.

Enter both equations from Part 1 into the Desmos Graphing Calculator and write down the intersection point.  You may need to zoom in to see the intersection._______ 

3.4 Manipulating Equations

3.4 Manipulating Equations

Solve for d:

Solve for y

Solve for k

Solve for y

Solve for x

Solve for r
*type pi and it will change to the symbol for pi

Solve for w

Solve for y

Solve for y

Solve for P:

Solve for r:

Solve for t:

Part II: Reflection
What does this intersection point represent in the context of the original problem?

Do you think that investing your money into these accounts was worth it? Why or why not?

What else could you have done with your money instead of keeping it in a savings account?

What does this intersection point represent in the context of the original problem?

Were the interest rates that you calculated in this word problem higher or lower than what they currently are in the real world?

Do you think savings accounts are a good way to earn money on your deposits? Why or why not?

Solve for d:

Solve for y

Solve for k

Solve for y

Solve for x

Solve for r
*type pi and it will change to the symbol for pi

Solve for w

Solve for y

Solve for y

Solve for P:

Solve for r:

Solve for t:

Part II: Reflection
What does this intersection point represent in the context of the original problem?

Do you think that investing your money into these accounts was worth it? Why or why not?

What else could you have done with your money instead of keeping it in a savings account?

What does this intersection point represent in the context of the original problem?

Were the interest rates that you calculated in this word problem higher or lower than what they currently are in the real world?

Do you think savings accounts are a good way to earn money on your deposits? Why or why not?

3.4 Manipulating Equations

3.4 Manipulating Equations

Solve for d:

Solve for y

Solve for k

Solve for y

Solve for x

Solve for r*type pi and it will change to the symbol for pi

Solve for w

Solve for y

Solve for y

Solve for P:

Solve for r:

Solve for t:

Part II: ReflectionWhat does this intersection point represent in the context of the original problem?

Do you think that investing your money into these accounts was worth it? Why or why not?

What else could you have done with your money instead of keeping it in a savings account?

What does this intersection point represent in the context of the original problem?

Were the interest rates that you calculated in this word problem higher or lower than what they currently are in the real world?

Do you think savings accounts are a good way to earn money on your deposits? Why or why not?

Solve for d:

Solve for y

Solve for k

Solve for y

Solve for x

Solve for r*type pi and it will change to the symbol for pi

Solve for w

Solve for y

Solve for y

Solve for P:

Solve for r:

Solve for t:

Part II: ReflectionWhat does this intersection point represent in the context of the original problem?

Do you think that investing your money into these accounts was worth it? Why or why not?

What else could you have done with your money instead of keeping it in a savings account?

What does this intersection point represent in the context of the original problem?

Were the interest rates that you calculated in this word problem higher or lower than what they currently are in the real world?

Do you think savings accounts are a good way to earn money on your deposits? Why or why not?

Solve for r
*type pi and it will change to the symbol for pi

Part II: Reflection
What does this intersection point represent in the context of the original problem?

Solve for r
*type pi and it will change to the symbol for pi

Part II: Reflection
What does this intersection point represent in the context of the original problem?