Objective: Solve Money Word Problems in One Variable

Algebra Mrs. von Stein

Lesson #13 Name:

Objective: Solve Money Word Problems in one variable

A.A. 22 Solve all types of linear equations in one variable

WARM – UP

1. The members of the senior class are planning a dance.

They use the equation r = pn to determine the total receipts.

What is n expressed in terms of r and p?

A) n = r + p

B) n = r – p

C) n=pr

D) n=rp

2. John’s father weighs 20 pounds more than twice what John weighs. If John’s weight is

represented by y, then his father’s weight may be represented by:

A) 2y

B) 2y – 20

C) 2y + 20

D) 12y+20

Example 1:

Jane bought a pencil and received change for $3.00 in 20 coins, all nickels and quarters.

How many of each kind are given?

Solution:

Step 1: Write Let Statements

Let q = number of quarters

20 – q = number of nickels

Total = quantity x value

Step 2: Set up a table with quantity and value.

Step 3: Add down the last column to get the equation and solve.

Example 2

John received change worth $13. He received 10 more dimes than nickels and 22 more quarters than dimes. How many coins of each did he receive?

Step 1: Let

Step2: Set up a table with quantity and value.

Step 3: Add down the last column to get the equation and solve.

Practice:

1. Paul has $31.15 from paper route collections. He has 5 more nickels than quarters and 7 fewer

dimes than quarters. How many of each coin does Paul have?

Example 3

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: Write Let statements for quantities of stamps

Let x = number of $0.15 stamps

50 – x = number of $0.20 stamps

Total = quantity x value

Step 2: Set up a table with quantity and value

Step 3: Add down the last column to get the equation and solve

Example 4

The cost of tickets for a play is $3.00 for adults and $2.00 for children. 350 tickets were sold and $950 was collected. How many tickets of each type were sold?

Step 1:

Write Let statements for the variables.

Let x = number of $3.00 tickets

350 – x = number of $2.00 tickets

Total = quantity x value

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

Step 3: Add down the last column to get the equation and solve.

Practice:

2. Jim sold 120 tickets to a game. Adult tickets are $24 each and children tickets are $13 each. Sales are $2110.

How many of each was sold?

3. 500 people see a play. Children are charged $15 and adults $25. Tickets proceeds are $11,250.

How many children attended the play?

Challenge:

Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. You’re not too interested until he tells you that he’s been collecting these gold-tone one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin does he have?

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EXIT TICKET:

NAME: ______Period: ______

A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?

Answer to Challenge:

25q + 100(26 – q) = 1700

25q + 2600 – 100q = 1700

-75q + 2600 = 1700 – 75q

-75q = -900

q = 12

12 of the coins are quarters. Since the remainder of the twenty-six coins are dollar coins, there are 26 – 12 = 14 dollar coins.

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