Solve Money Applications: example 9.12

Maria has $$2.43$ in quarters and pennies in her wallet. She has twice as many pennies as quarters. How many coins of each type does she 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.

1
Solution
Step 1. Read the problem.
- Determine the types of coins involved.
  We know that Maria has quarters and pennies.
- 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.
Type $Number$ $Value ($)$ $Total Value ($)$

Quarters $0.25$

Pennies $0.01$

$2.43$

Step 2. Identify what you are looking for.
$We are looking for the number of quarters and pennies.$

Step 3. Name: Represent the number of quarters and pennies using variables.
$We know Maria has twice as many pennies as quarters. The number of pennies is defined in terms of quarters.$

$Let q represent the number of quarters.$

$Then the number of pennies is 2 q .$

Type $Number$ $Value ($)$ $Total Value ($)$

Quarters $q$ $0.25$

Pennies $2 q$ $0.01$

$2.43$

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

Type $Number$ $Value ($)$ $Total Value ($)$

Quarters $q$ $0.25$ $0.25 q$

Pennies $2 q$ $0.01$ $0.01 (2 q)$

$2.43$

Step 4. Translate. Write the equation by adding the 'total value’ of all the types of coins.
Step 5. Solve the equation.

Write the equation.

Multiply.

Combine like terms.

Divide by 0.27.

The number of pennies is 2q.

Step 6. Check the answer in the problem.
Maria has $9$ quarters and $18$ pennies. Does this make $$2.43 ?$

$\begin{matrix} 9 quarters & 9 (0.25) & = & 2.25 \\ 18 pennies & 18 (0.01) & = & \underset{_____}{0.18} \\ Total & $2.43 ✓ \end{matrix}$

Step 7. Answer the question. Maria has nine quarters and eighteen pennies.

Type	$Number$	$Value ($)$
Quarters		$0.25$
Pennies		$0.01$
	$2.43$

Type	$Number$	$Value ($)$
Quarters	$q$	$0.25$
Pennies	$2 q$	$0.01$
	$2.43$

Type	$Number$	$Value ($)$	$Total Value ($)$
Quarters	$q$	$0.25$	$0.25 q$
Pennies	$2 q$	$0.01$	$0.01 (2 q)$
	$2.43$

Your turn

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

Sumanta has $$4.20$ in nickels and dimes in her desk drawer. She has twice as many nickels as dimes. How many coins of each type does she have?

How did it go?

Write the equation.
Multiply.
Combine like terms.
Divide by 0.27.
The number of pennies is 2q.

Solution

Your turn