9.2 Solve money applications  (Page 3/5)

Solution

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.

Step 5. Solve the equation.

How many nickels?

Step 6. Check. Is the total value of $4$ pennies and $42$ nickels equal to $\text{\$2.14}?$

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

Solution

Step 1: Read the problem.

• Determine the types of tickets involved.
  There are student tickets and adult tickets.
• Create a table to organize the information.

Step 2. Identify what you are looking for.

$\text{We are looking for the number of student and adult tickets.}$

Step 3. Name. Represent the number of each type of ticket using variables.

$\text{We know the number of adult tickets sold was}5\text{less than three times the number of student tickets sold.}$

$\text{Let}s\text{be the number of student tickets.}$

$\text{Then}3s-5\text{is the number of adult tickets.}$

$\text{Multiply the number times the value to get the total value of each type of ticket.}$

Step 4. Translate: Write the equation by adding the total values of each type of ticket.

Step 5. Solve the equation.

Substitute to find the number of adults.

Step 6. Check. There were $47$ student tickets at $\text{\$6}$ each and $136$ adult tickets at $\text{\$9}$ each. Is the total value $\text{\$1506}?$ We find the total value of each type of ticket by multiplying the number of tickets times its value; we then add to get the total value of all the tickets sold.

Step 7. Answer the question. They sold $47$ student tickets and $136$ adult tickets.