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Money Problems:

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Money Problems:

By

Dr. Marcia Tharp and

Dr. Julia Arnold

In money problems we encounter two types of numbers:

For example, if we say “the number of coins is 6”, 6 represents how many coins. If we say the value of the coins is 60 cents, then 60 represents how much the coins are worth.

The two ideas are:

how many

and

value of

See if you can pick out the the number for how many, and the number for the value of in the next problem.

The Hurrah Players sold 600 tickets to a recent event. Adults paid $5 each and students paid $2 each. If the total collected was $2025, how many tickets of each type were sold?

600 is how many

$5, $2, and $2025 represents the value of

If you have 5 nickels, what is the value of the money?

25 cents

If you have $3.00 in dimes, how many dimes do you have?

30

How did you get the numbers above?

In the nickel problem you multiplied the “number of” by the “value of” and thus 5 * .05 = .25 = 25 cents

In the dime problem you divided the value of the money by the value of one dime dimes

The Hurrah Players sold 600 tickets to a recent event. Adults paid $5 each and students paid $2 each. If the total collected was $2025, how many tickets of each type were sold?

R Read the problem over and over until you feel you understand the problem.

You might make a casual guess.

250 adult and 350 student tickets for example

1.

How could you check your guess?

By multiplying the “how many” number by the “value of” number.

250 * $5 + 350 * $2 = $1950

Since the total is not $2025 we know this guess isn’t right.

I’m ready to get this problem done so algebra is going to be a lot quicker than guessing.

Let’s chart the information as follows:

This is the information I have!

How many

Value of

Total

Tickets

5

Adult

Student

2

Total

600

2025

How many

Value of

Total

Tickets

x

5

Adult

Student

2

Total

600

2025

Now let’s add the algebra.

Since the number of adult tickets is unknown, let

# of adult tickets = x

How would we represent the number of student tickets?

If you said x, that would make x = 300 automatically since x also represents adult tickets. Not right.

How many

Value of

Total

Tickets

x

5

Adult

Student

2

Total

600

2025

How would we represent the number of student tickets?

When you know a total (600) and x represents part of that total, use subtraction total - part

600-x = number of student tickets.

600 - x

How many

Value of

Total

Tickets

x

5

Adult

Student

2

Total

600

2025

Now we must multiply “how many” by “value of” and put in total column.

5x

2(600 - x)

600 - x

Form the equation.

The money from the student tickets and the money from the adult tickets should add up to equal the total amount collected.

cost adult tickets + cost student tickets = total collected

5x + 2(600 – x) = 2025

5x + 1200 - 2x = 2025

3x + 1200 = 2025

3x = 825

x = 275 adult tickets

600 - 275 = 325 student tickets

Its your turn to practice money problems.

Directions: work out problems 1-6 then check the solutions found on next slide.

1. Yolanda has dimes and quarters totaling $5.25. If she has 33 coins in all how many of each does she have?

2. Tony has 39 bills in fives and tens. If the total value is $285 how many of each does he have?

3. The Drama Club sold 500 tickets to their fall performance. The adult tickets were $5 each and the student tickets were $3 each. If they took in $2080, how many of each did they sell?

4. Edie has 27 coins in dimes and quarters. If the total value is $3.75 how many of each does she have?

5. Venus bought 40 stamps for $12.40. Some of the stamps were 33-cent stamps and some were 23 cent stamps. How many of each did she buy?

6. Sonia has 26 bills in ones and fives. If their total value is $50 how many of each does she have?

Answers to Practice Problems

- 20 dimes and 13 quarters
- 21 fives and 18 tens
- 290 adult tickets and 210 student tickets
- 20 dimes and 7 quarters
- 32 stamps at 33cents each and 8 stamps at 23 cents each
- 20 $1 bills and 6 $5 bills

Complete Solutions Follow

1. Yolanda has dimes and quarters totaling $5.25. If she has 33 coins in all how many of each does she have?

.10x + .25(33-x)= 5.25

.10x +8.25 - .25x=5.25

-.15x=-3

x = 20 dimes

33-x = 13 quarters

Total 33 coins $5.25

The equation is the sum of the last column =‘s total or

.10x + .25(33-x)= 5.25

2. Tony has 39 bills in fives and tens. If the total value is $285 how many of each does he have?

5x + 10(39 – x)= 285

5x + 390 –10x =285

-5x = -105

x = 21 fives

39-x = 18 tens

Total 39 bills $285

The equation is the sum of the last column =‘s total or

5x + 10(39 – x)= 285

3. The Drama Club sold 500 tickets to their fall performance. The adult tickets were $5 each and the student tickets were $3 each. If they took in $2080, how many of each did they sell?

5x + 3(500 – x)= 2080

5x + 1500 –3x =2080

2x = 580

x = 290 adult tickets

500-x = 210 student

tickets

Total 500 tickets $2080

The equation is the sum of the last column =‘s total or

5x + 3(500 – x)= 2080

4. Edie has 27 coins in dimes and quarters. If the total value is $3.75 how many of each does she have?

.10x +.25(27 – x) = 3.75

.10x +6.75 - .25x =3.75

-.15x = -3

x = 20 dimes

27-x = 7 quarters

Total 27 coins $3.75

The equation is the sum of the last column =‘s total or

.10x +.25(27 – x) = 3.75

5. Venus bought 40 stamps for $12.40. Some of the stamps were 33-cent stamps and some were 23 cent stamps. How many of each did she buy?

.33x + .23(40-x)=12.40

.33x +9.2 -.23x=12.40

.10x = 3.20

x = 32 33 cent stamps

40-x = 8 23 cent

stamps

Total 40 stamps $12.40

The equation is the sum of the last column =‘s total or

.33x + .23(40-x)=12.40

6. Sonia has 26 bills in ones and fives. If their total value is $50 how many of each does she have?

x + 5(26 – x)=50

X + 130 –5x = 50

-4x = -80

X = 20 ones

26 – x = 6 fives

Total 26 bills $50

The equation is the sum of the last column =‘s total or

x + 5(26 – x)=50

Now its time to go to the Mixture Problems