ExerciseWhat is the value of seven nickels?

$0.35

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

Exercise

Money ProblemsIn the first type of problem, the total number of coins is known. The total value of the money is not.

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?

Example 1

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.

CoinDimes

Quarters

Number of Coinsd

2d + 3

d + (2d + 3) = 351(d + 2d) + 3 = 351

3d + 3 = 3513d + 3 – 3 = 351 – 3

3d = 3483 3d = 116 dimes

351 – 116 = 235 quarters116(0.10) + 235(0.25)

= $70.35

116 dimes

Money ProblemsIn the second type of money problem, the total value of the money is known, but the number of coins of each denomination is not.

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.

Example 2

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

NickelsDimes

# of Coins

3p + 183p

Pennies p510

15(3p + 18)

10(3p)

p

Value of

CoinsTotal Value

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 = 1,42446p + 90 = 1,424

46p + 90 – 90 = 1,424 – 9046p = 1,33446 46

p = 29 pennies3p = 3(29) = 87 dimes3p + 18 = 3(29) + 18

= 105 nickels

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?

Example 3

Coin

DimesQuarters

# of Coins

2nn + 3

Nickels n1025

510(2n)

25(n + 3)

5n

Value of

CoinsTotal Value

5n + 10(2n) + 25(n + 3) = 4755n + 20n + 25n + 75 = 475

50n + 75 = 47550n + 75 – 75 = 475 – 75

50n = 40050 50

n = 8 nickels2n = 2(8) = 16 dimesn + 3 = 8 + 3 = 11 quarters

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?

Example 4

Coin

Quarters

# of Coins

qNickels 29 – q

255

25q5(29 – q)

Value of

CoinsTotal Value

5(29 – q) + 25q = 485

q = 17 quarters29 – q = 29 – 17 = 12 nickels

145 – 5q + 25q = 485145 + 20q = 485

145 – 145 + 20q = 485 – 14520q = 34020 20

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

16 pennies, 32 nickels, 24 dimes, and 48 quarters

ExampleIf the number of dimes is half the total number of nickels and pennies, how many of each does he have?

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.

Example

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

Exercise