Example 9.13 from Prealgebra, 9.2 Solve Money Applications

Solve Money Applications: example 9.13

Danny has $$2.14$ worth of pennies and nickels in his piggy bank. The number of nickels is two more than ten times the number of pennies. How many nickels and how many pennies does Danny have?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution

Step 1: Read the problem.
Determine the types of coins involved. Create a table.	Pennies and nickels
Write in the value of each type of coin.	Pennies are worth $$0.01.$ Nickels are worth $$0.05.$
Step 2: Identify what you 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.	Let $p = number of pennies$
The number of nickels is two more than then times the number of pennies.	$10 p + 2 = number of nickels$

Multiply the number and the value to get the total value of each type of coin.

Type	$Number$	$Value ($)$	$Total Value ($)$
pennies	$p$	$0.01$	$0.01 p$
nickels	$10 p + 2$	$0.05$	$0.05 (10 p + 2)$
			$$2.14$

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. Is the total value of $4$ pennies and $42$ nickels equal to $$2.14 ?$

\begin{matrix} 4 (0.01) + 42 (0.05) \overset{?}{=} 2.14 \\ 2.14 = 2.14 ✓ \end{matrix}

Step 7. Answer the question. Danny has $4$ pennies and $42$ nickels.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Jesse has $$6.55$ worth of quarters and nickels in his pocket. The number of nickels is five more than two times the number of quarters. How many nickels and how many quarters does Jesse have?

How did it go?