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.
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?
Step 1: Set up a table with quantity and value.
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
Step 3: Add down each column to get the equations
x + y = 50 (equation 1)
15x + 20y = 950 (equation 2)
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.
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