Answer:
Imagine taking a handful of coins from your pocket or purse and placing them on your desk. How would you determine the value of that pile of coins?
If you can form a step-by-step plan for finding the total value of the coins, it will help you as you begin solving coin word problems.
One way to bring some order to the mess of coins would be to separate the coins into stacks according to their value. Quarters would go with quarters, dimes with dimes, nickels with nickels, and so on. To get the total value of all the coins, you would add the total value of each pile.
How would you determine the value of each pile? Think about the dime pile—how much is it worth? If you count the number of dimes, you’ll know how many you have—the number of dimes.
But this does not tell you the value of all the dimes. Say you counted
17
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
17
dimes, multiply
17
by
$0.10
to get
$1.70
. This is the total value of all
17
dimes.
You could continue this process for each type of coin, and then you 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.
Let’s look at a specific case. Suppose there are
14
quarters,
17
dimes,
21
nickels, and
39
pennies. We’ll make a table to organize the information – the type of coin, the number of each, and the value.
The total value of all the coins is
$6.64
. Notice how the above table helped us organize all the information.
Let’s review the problem-solving method for word problems.
PROBLEM-SOLVING STRATEGY
Step 1. Read the problem. Make sure you understand all the words and ideas.
Step 2. Identify what you are looking for.
Step 3. Name what you are looking for.
Step 4. Translate into an equation. Restate the problem in one sentence. Then translate into an equation.
Step 5. Solve the equation using good algebra techniques.
Step 6. Check.
Step 7. Answer the question.
