Key Concepts

Key Concepts

• Total Value of Coins For the same type of coin, the total value of a number of coins is found by using the model.
  \(number·value=total\phantom{\rule{0.2em}{0ex}}value\) where number is the number of coins and value is the value of each coin; total value is the total value of all the coins
• Problem-Solving Strategy—Coin Word Problems
  
  1. Read the problem. Make all the words and ideas are understood. Determine the types of coins involved.
     
     • Create a table to organize the information.
     • Label the columns type, number, value, total value.
     • List the types of coins.
     • Write in the value of each type of coin.
     • Write in the total value of all the coins.
  2. Identify what we are looking for.
  3. Name what we are looking for. Choose a variable to represent that quantity.
     Use variable expressions to represent the number of each type of coin and write them in the table.
     Multiply the number times the value to get the total value of each type of coin.
  4. Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the sentence into an equation.
     Write the equation by adding the total values of all the types of coins.
  5. Solve the equation using good algebra techniques.
  6. Check the answer in the problem and make sure it makes sense.
  7. Answer the question with a complete sentence.

Glossary

mixture problems

Mixture problems combine two or more items with different values together.