3.4 Manipulating Equations

CALCULATE: Solving equations

Solve each of the following equations for x.

SHOW YOUR WORK FOR FULL CREDIT

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*

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.

1. 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

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

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.

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

1. 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.