Transcript Applied Problems: - Tidewater Community College

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.
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
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 3.00  30 dimes
.10
R
Read the problem over and over until you feel
you understand the 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?
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!
Tickets
How many
Value of
Adult
5
Student
2
Total
600
Total
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.
Tickets
Adult
How many
x
Student
Total
Value of
Total
5
2
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.
Tickets
Adult
Student
Total
How many
x
600 - x
600
Value of
Total
5
2
2025
Now we must multiply “how many” by “value of” and put
in total column.
Tickets
Adult
Student
Total
How many
x
600 - x
600
Value of
5
2
Total
5x
2(600 - x)
2025
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
1.
2.
3.
4.
5.
6.
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?
Number Value of Total
Multiply
Of Coins Coins
previous two
columns
Dimes
x
.10
.10x
quarters
33-x
.25
.25(33-x)
Total
33 coins
.10x + .25(33-x)= 5.25
.10x +8.25 - .25x=5.25
-.15x=-3
x = 20 dimes
33-x = 13 quarters
$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?
Number
Of Bills
Value of Total
Multiply
Bills
previous two
columns
Fives
x
5
5x
Tens
39-x
10
10(39-x)
Total
39 bills
5x + 10(39 – x)= 285
5x + 390 –10x =285
-5x = -105
x = 21 fives
39-x = 18 tens
$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?
Number
Of Tickets
Cost of a
Ticket
Total
Multiply
previous two
columns
Adult
x
5
5x
Student
500-x
3
3(500-x)
Total
500 tickets
5x + 3(500 – x)= 2080
5x + 1500 –3x =2080
2x = 580
x = 290 adult tickets
500-x = 210 student
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?
Number
Of Tickets
Dimes
x
Quarters 27-x
Total
27 coins
Cost of a
Ticket
Total
Multiply
previous two
columns
.10
.10x
.25
.25(27-x)
.10x +.25(27 – x) = 3.75
.10x +6.75 - .25x =3.75
-.15x = -3
x = 20 dimes
27-x = 7 quarters
$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?
Number
Of Tickets
Cost of a
Ticket
Total
Multiply
previous two
columns
33 cent
stamps
x
.33
.33x
23 cent
40-x
.23
.23(40-x)
Total
40 stamps
.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
$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?
Number
Of Tickets
Cost of a
Ticket
Total
Multiply
previous two
columns
ones
x
1
x
fives
26-x
5
5(26-x)
Total
26 bills
x + 5(26 – x)=50
X + 130 –5x = 50
-4x = -80
X = 20 ones
26 – x = 6 fives
$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