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Algebra: Stamp Word Problems




 
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Stamp problems are algebra word problems that are very similar to coin problems and ticket problems in that stamps are denominated in specific values.

Be careful to distinguish between the value of the items and the quantity of the items. A table is useful for distinguishing between quantity and value in this type of word problems.

Example 1:

John has 50 stamps, some worth 15¢ and some worth 20¢. If their value is $9.50, how many of each kind does John have?

Solution:

Step 1: Set up a table with quantity and value.

 

quantity

value

total

15¢ stamps

     

20¢ stamps

     

together

     

Step 2: Fill in the table with information from the question.

John has 50 stamps, some worth 15¢ and some worth 20¢. If their value is $9.50, how many of each kind does John have?

Let x =   number of 15¢ stamps
  y =   number of 20¢ stamps
  Total =   quantity × value

 

quantity

value

total

15¢ stamps

x

15¢

15x

20¢ stamps

y

20¢

20y

together

50

 

950

Step 3: Add down each column to get the equations

x + y = 50                 (equation 1)
15x + 20y = 950        (equation 2)

Use Substitution Method
Isolate variable x in equation 1

x = 50 – y                  (equation 3)

Substitute equation 3 into equation 2

15(50 – y) + 20y = 950
750 – 15y + 20y = 950
20y – 15y = 950 – 750
5y = 200
y = 40

Substitute y = 40 into equation 1

x + 40 = 50
x = 10

Answer: John has ten 15¢ stamps and forty 20¢ stamps.




Stamp Problem
Shows how to solve a word problem having to do with different stamps and their values. This is solved with one variable, but more than one stamp is defined. It is done with a chart.
Example: Jerry has some 3 cents stamps and 29 cents stamps worth $1.54. The number of 29 cents stamps is four less than three times the number of 3 cents stamps. How many 29 cents stamps does he have?
Stamp Word Problem - 2 variable system of equations
We solve this word problem using a system of equations with 2 variables.
Example: Juan has 80 stamps. Some were 29¢ stamps and some were 45¢ stamps. The total value of all the stamps was $27.04. How many of each type of stamp does he have?
Define 2 variables, set up a system of equations, use algebra to solve, and check.


 

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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