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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?

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.

The number of nickels is two more than then times the number of pennies.

Let p = 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 ?

4 ( 0.01 ) + 42 ( 0.05 ) = ? 2.14 2.14 = 2.14

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

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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?

41 nickels, 18 quarters

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Elaine has $7.00 in dimes and nickels in her coin jar. The number of dimes that Elaine has is seven less than three times the number of nickels. How many of each coin does Elaine have?

22 nickels, 59 dimes

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Solve ticket and stamp word problems

The strategies we used for coin problems can be easily applied to some other kinds of problems too. Problems involving tickets or stamps are very similar to coin problems, for example. Like coins, tickets and stamps have different values; so we can organize the information in tables much like we did for coin problems.

At a school concert, the total value of tickets sold was $1,506 . Student tickets sold for $6 each and adult tickets sold for $9 each. The number of adult tickets sold was 5 less than three times the number of student tickets sold. How many student tickets and how many adult tickets were sold?

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.
Type Number Value ($) Total Value ($)
Student 6
Adult 9
1,506

Step 2. Identify what you are looking for.

We are looking for the number of student and adult tickets.

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

We know the number of adult tickets sold was 5 less than three times the number of student tickets sold.

Let s be the number of student tickets.

Then 3 s 5 is the number of adult tickets.

Multiply the number times the value to get the total value of each type of ticket.

Type Number Value ($) Total Value ($)
Student s 6 6 s
Adult 3 s 5 9 9 ( 3 s 5 )
1,506

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

6 s + 9 ( 3 s 5 ) = 1506

Step 5. Solve the equation.

6 s + 27 s 45 = 1506 33 s 45 = 1506 33 s = 1551 s = 47 students

Substitute to find the number of adults.

The top line says 3s minus 5 equals number of adults. The bottom line shows 3 times a red 47 minus 5 equals 136 adults.

Step 6. Check. There were 47 student tickets at $6 each and 136 adult tickets at $9 each. Is the total value $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.

47 · 6 = 282 136 · 9 = 1224 _____ 1506

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

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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