Section 1.5Applications Linear Equations 1-Var.

HOMEWORK: 1.5 3 – 63 odd

Important formulas:

Sales Tax: (cost of merchandise)(tax rate)

Commission: (dollars in sales)(rate)

Simple Interest:I = Prt

Distance = (rate)(time)d=rt

Strategy or solving Applications:

  1. Read the problem carefully.
  2. Identify what you know and what you want to find. Assign labels to known quantities and variables to unknown quantities. It is often useful to organize the information in a table and/or draw a picture.
  3. Develop a verbal model
  4. Write a mathematical equation
  5. Solve the equation
  6. Interpret the results and write final answer in words. Include units is appropriate.

Examples involving #’s:

Example 1. The sum of two numbers is 40. One number is 5 less than twice the other number. What are the numbers?

Step 1: Read

Step 2: Assign labels to unknown quantities

Step 3: Develop a verbal model

(One Number) + (Other Number) =

Step 4: Mathematical Equation

Step 5: Solve

Step 6: Interpret the results:

Sometimes numerical applications will involve consecutive numbers. Consecutive numbers are numbers that follow one after the other in order.

For Example, 5 and 6 are consecutive integers.

The numbers 6, 8, 10 are consecutive even integers.

The numbers 3, 5, 7 and consecutive odd integers.

Examples of Applications involving rates:

Often in many real world situations, percents are used to represent rates. When working with %, we must convert to a decimal to solve the problem.

Example: Suppose you invest $6000 in an account that pays 5 ¾ % simple interest to pay next semesters tuition. How much will you in the account in 4 months when you plan to withdraw the money?

Recall:

Interest = (Principal)(annual interest rate)(time in years)

Or

I=Prt

The total in the account should be the initial amount plus the interest earned!

Example 2: The bookstore uses the standard 40% mark-up on all books purchased wholesale from the publisher. If your book cost $135.00 at the bookstore, that was the wholesale cost?

(Selling price = original price + markup)

Example 3: Suppose you took out 2 different school loans for a total amount of $16000. The first the first loan charged 7% interest and the other charged 15% interest. At the end of the first year, you paid a total of 1440 in interest. How much was borrowed in each loan?

7% / 15% / Total
Amt borrowed
Amt interest paid

Mixture problems:

Example: How many liters (L) of a 60% juice mixture should be added to 5 L of a 10% juice solution to produce a 25% juice mixture?

60% / 10% / Final 25%
# L of solution
# L of pure juice

Distance, Rate and time:

Recall distance = (rate)(time) or d=rt

Example: A woman can hike 1 mph faster down a trail to Lake Michigan than she can on the return trip uphill. It takes her 3 hr to get to the lake and 6 hours to return. What was her speed each direction?

Distance / Rate / Time
Trip to Lake
Return trip

Additional Examples:

Mixture problems:

Example: A small truck has a radiator that holds 20 liters. A mechanic needs to fill the radiator with a solution that is 60% antifreeze. He has 70% and 30% antifreeze solutions. How many liters of each should he use to achieve the desired mix?

70% / 30% / Final 60%
# L of solution
# L of pure antifreeze

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