Answer:
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.
Example1:
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
Let 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.
Step-by-step explanation:
