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.

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Money problems

Money Problems:

By

Dr. Marcia Tharp and

Dr. Julia Arnold


Money problems

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.


Example 1

Example 1

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


Money problems

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


Money problems

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.


Money problems

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


Money problems

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.


Money problems

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


Money problems

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


Money problems

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


Money problems

Its your turn to practice money problems.


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?


Money problems

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?


Money problems

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


Money problems

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


Money problems

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


Money problems

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


Money problems

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


Money problems

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


Money problems

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


Money problems

Now its time to go to the Mixture Problems


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