Solving Linear Equations
Solve Mixture and Uniform Motion Applications
Learning Objectives
By the end of this section, you will be able to:
- Solve coin word problems
- Solve ticket and stamp word problems
- Solve mixture word problems
- Solve uniform motion applications
Before you get started, take this readiness quiz.
- Simplify:
If you missed this problem, review (Figure).
- The number of adult tickets is three more than twice the number of children tickets. Let c represent the number of children tickets. Write an expression for the number of adult tickets.
If you missed this problem, review (Figure).
- Convert 4.2% to a decimal.
If you missed this problem, review (Figure).
Solve Coin Word Problems
Using algebra to find the number of nickels and pennies in a piggy bank may seem silly. You may wonder why we just don’t open the bank and count them. But this type of problem introduces us to some techniques that will be useful as we move forward in our study of mathematics.
If we have a pile of dimes, how would we determine its value? If we count the number of dimes, we’ll know how many we have—the number of dimes. But this does not tell us the value of all the dimes. Say we counted 23 dimes, how much are they worth? Each dime is worth ?0.10—that is the value of one dime. To find the total value of the pile of 23 dimes, multiply 23 by ?0.10 to get ?2.30.
The number of dimes times the value of each dime equals the total value of the dimes.
This method leads to the following model.
For the same type of coin, the total value of a number of coins is found by using the model
- number is the number of coins
- value is the value of each coin
- total value is the total value of all the coins
If we had several types of coins, we could continue this process for each type of coin, and then we would know the total value of each type of coin. To get the total value of all the coins, add the total value of each type of coin.
Jesse has ?3.02 worth of pennies and nickels in his piggy bank. The number of nickels is three more than eight times the number of pennies. How many nickels and how many pennies does Jesse have?
| Step 1. Read the problem.
Determine the types of coins involved. Create a table. Write in the value of each type of coin. |
pennies and nickels Pennies are worth ?0.10. Nickels are worth ?0.05. |
| Step 2. Identify what we are looking for. | the number of pennies and nickels |
| Step 3. Name. Represent the number of each type of coin using variables.
The number of nickels is defined in terms of the number of pennies, so start with pennies. The number of nickels is three more than eight times the number of pennies. |
Let number of pennies. number of nickels |
| In the chart, multiply the number and the value to
get the total value of each type of coin. |
|
| Step 4. Translate. Write the equation by adding the total value of all the types of coins. |
|
| Step 5. Solve the equation. | |
| How many nickels? | |
| Step 6. Check the answer in the proble