Exercise
What is the value of seven
nickels?
$0.35
Exercise
What is the value of fourteen
quarters?
$3.50
Exercise
Write two expressions for the
value of d dimes, one in
dollars and one in cents.
0.1d and 10d
Exercise
Joe has 23 coins in his
pocket. He has 7 nickels, and
the rest of the coins are an
equal number of dimes and
quarters. How much money
does he have?
$3.15
Exercise
Shannon has twice as many
quarters as dimes; and the
total number of her dimes,
quarters, and pennies is 12.
Write expressions for the
numbers of quarters and
pennies in terms of d, the
number of dimes.
quarters: 2d; pennies: 12 – 3d
Money Problems
In the first type of problem,
the total number of coins is
known. The total value of the
money is not.
Example 1
Ivan has been saving money
and has 351 coins. He has
three more quarters than
twice the number of dimes.
How many of each coin does
he have? How much money
does he have?
Since the number of quarters
is expressed in terms of the
number of dimes, let d
represent the number of dimes.
Then express the number of
quarters in terms of d.
Coin
Dimes
Quarters
Number of Coins
d
2d + 3
d + (2d + 3) = 351
(d + 2d) + 3 = 351
3d + 3 = 351
3d + 3 – 3 = 351 – 3
3d = 348
3
3
d = 116 dimes
116 dimes
351 – 116 = 235 quarters
116(0.10) + 235(0.25)
= $70.35
Money Problems
In the second type of money
problem, the total value of
the money is known, but the
number of coins of each
denomination is not.
Example 2
Steve saves money by putting
his dimes, nickels, and
pennies in a jar. He has three
times as many dimes as
pennies and 18 more nickels
than dimes. If he has a total of
$14.24, find the number of
dimes, nickels, and pennies
he has.
Notice that the number of
dimes is described in terms of
the number of pennies, and the
number of nickels is described
in terms of the number of
dimes. It would be best to
know the number of pennies
first. Let p = the number of
pennies.
Coin
Pennies
Value
# of
of
Coins Coins
p
Nickels 3p + 18
Dimes
3p
Total
Value
1
p
5
5(3p + 18)
10
10(3p)
Each dollar is 100 cents, so he
has 14.24(100) = 1,424 cents.
This number will be used in the
equation since the values of
the coins in the table are given
in cents.
p + 5(3p + 18) + 10(3p) = 1,424
p + 15p + 90 + 30p = 1,424
46p + 90 = 1,424
46p + 90 – 90 = 1,424 – 90
46p = 1,334
46
46
p = 29 pennies
3p = 3(29) = 87 dimes
3p + 18 = 3(29) + 18
= 105 nickels
Example 3
Shyla has twice as many
dimes as nickels, and she
has three more quarters than
nickels. If her coins total
$4.75, how many of each
coin does she have?
Value
#
of
Total
Coin
of
Coins
Value
Coins
5n
n
Nickels
5
2n
10(2n)
Dimes
10
Quarters n + 3
25 25(n + 3)
5n + 10(2n) + 25(n + 3) = 475
5n + 20n + 25n + 75 = 475
50n + 75 = 475
50n + 75 – 75 = 475 – 75
50n = 400
50
50
n = 8 nickels
2n = 2(8) = 16 dimes
n + 3 = 8 + 3 = 11 quarters
Example 4
George has 29 coins, made
up of quarters and nickels. If
their total value is $4.85, how
many of each coin does he
have?
Coin
Value
# of
of
Coins Coins
Total
Value
Nickels
29 – q
5
5(29 – q)
Quarters
q
25
25q
5(29 – q) + 25q = 485
145 – 5q + 25q = 485
145 + 20q = 485
145 – 145 + 20q = 485 – 145
20q = 340
20
20
q = 17 quarters
29 – q = 29 – 17 = 12 nickels
Example
Joe has 50 nickels and
dimes. The number of dimes
is five more than twice the
number of nickels. How
many of each does he have?
Example
15 nickels and 35 dimes
Example
Lucy has 70 nickels, dimes,
and quarters. The number of
dimes is five more than twice
the number of nickels, and
the number of quarters is
five more than three times
the number of nickels.
Example
How many of each does she
have?
10 nickels, 25 dimes, and 35
quarters
Example
Vern has 180 nickels, dimes,
and quarters. He has ten
more dimes than nickels and
as many quarters as he has
nickels and dimes combined.
How many of each does he
have?
Example
40 nickels, 50 dimes,
and 90 quarters
Example
Ricardo has 90 pennies,
nickels, and dimes. He has
twice as many nickels as
pennies and 50% more dimes
than nickels. How many of
each does he have?
Example
15 pennies, 30 nickels, and
45 dimes
Example
John has 120 coins in
pennies, nickels, dimes, and
quarters. He has twice as
many nickels as pennies and
twice as many quarters as
dimes.
Example
If the number of dimes is half
the total number of nickels
and pennies, how many of
each does he have?
16 pennies, 32 nickels, 24
dimes, and 48 quarters
Example
Gary has $421 in ones and
fives. The number of ones is
one more than twice the
number of fives. How many
of each does he have?
Example
60 fives and 121 ones
Example
Wren notices at the end of
the day that there is $4.10 in
change in the cash register
and, interesting enough, the
number of pennies, nickels,
dimes, and quarters are
exactly the same. How many
of each coin are there?
Example
10 of each
Example
Zhi withdraws $60 from the
bank each Friday so he will
have enough change for his
store’s cash registers over the
weekend. He always gets
twice as many nickels and
dimes as quarters...
Example
...and five times as many
pennies as quarters.
How many of each coin does
he get?
100 quarters, 200 dimes, 200
nickels, and 500 pennies
Example
Hans withdraws $255 from
his savings. He asks the
teller to give him twice as
many fives as ones and twice
as many tens as fives. How
many of each bill will he
receive?
Example
5 ones, 10 fives, and 20 tens
Example
Heidi wants to withdraw $3,500
from her savings. She asks
for five hundreds, and she
wants the rest to be divided
so she has the same number
of ones, fives, tens, and
twenties. Can this be done?
Example
n = 83.33; No, this cannot be
done since n is not an integer.
Exercise
Mr. Cohen’s net worth is
twice as much as Mr. Hall’s
and three times as much as
Mr. Chang’s. They claim that
their combined net worth is a
million dollars.
Exercise
Find the net worth of each
one to the nearest dollar.
Mr. Chang: $181,818;
Mr. Hall: $272,727;
Mr. Cohen: $545,455
Exercise
A roll of 36 bills contains two
more twenties than fifties,
eight fewer tens than
twenties, and twice as many
fives as fifties. How many of
each bill are in the roll? How
much money is in the roll of
bills?
Exercise
8 fifties, 10 twenties, 2 tens,
and 16 fives; $700