3.3 Solve mixture applications  (Page 2/10)

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.

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 .

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.

$\begin{array}{cccc}\begin{array}{c}\mathbf{\text{Step 5. Solve}}\text{the equation.}\hfill \\ \text{Multiply.}\hfill \\ \text{Combine like terms.}\hfill \\ \text{Divide by 0.27}\hfill \end{array}\hfill & & & \hfill \begin{array}{ccc}\hfill 0.25q+0.01(2q)& =\hfill & 2.43\hfill \\ \hfill 0.25q+0.02q& =\hfill & 2.43\hfill \\ \hfill 0.27q& =\hfill & 2.43\hfill \\ \hfill q& =\hfill & 9\text{quarters}\hfill \end{array}\hfill \\ \text{The number of pennies is}2q.\hfill & & & \hfill 2q\hfill \\ & & & \hfill 2·9\hfill \\ & & & \hfill \text{18 pennies}\hfill \\ \begin{array}{c}\mathbf{\text{Step 6. Check}}\text{the answer in the problem.}\hfill \\ \\ \\ \text{Maria has 9 quarters and 18 pennies. Does this}\hfill \\ \text{make \$2.43?}\hfill \end{array}\hfill & & & \\ \\ \\ \\ \\ \\ \begin{array}{cccccc}\text{9 quarters}\hfill & & & \hfill 9(0.25)& =\hfill & 2.25\hfill \\ \text{18 pennies}\hfill & & & \hfill 18(0.01)& =\hfill & \underset{\text{\_\_\_\_}}{0.18}\hfill \\ \text{Total}\hfill & & & & & \mathrm{\$2.43}✓\hfill \end{array}\hfill & & & \\ \mathbf{\text{Step 7. Answer}}\text{the question.}\hfill & & & \text{Maria has nine quarters and eighteen pennies.}\hfill \end{array}$