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.