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

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.

Carryonlearning

Answer:

17. 97 cakes

18. 68 stamps

19. 5,670pesos

20. 2 hours and 30 minutes