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

quarters: 2d; pennies: 12 – 3d 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 Number of Coins Dimes d Quarters 2d + 3

d + (2d + 3) = 351 (d + 2d) + 3 = 351 3d + 3 = 351 3d + 3 – 3 = 351 – 3 3d = 348 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.

Value of Coins # of Coins Total Value Coin Pennies p 1 p Nickels 3p + 18 5 5(3p + 18) Dimes 3p 10 10(3p)

Each dollar is 100 cents, so he has 14. 24(100) = 1,424 cents 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 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 Coins # of Coins Total Value Coin Nickels n 5 5n Dimes 2n 10 10(2n) 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 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?

Value of Coins # of Coins Total Value Coin 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 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.

10 nickels, 25 dimes, and 35 quarters 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?

40 nickels, 50 dimes, and 90 quarters 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?

15 pennies, 30 nickels, and 45 dimes 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.

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

100 quarters, 200 dimes, 200 nickels, and 500 pennies 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?

n = 83.33; No, this cannot be done since n is not an integer. 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.

Mr. Chang: $181,818; Mr. Hall: $272,727; Mr. Cohen: $545,455 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?

8 fifties, 10 twenties, 2 tens, and 16 fives; $700 Exercise 8 fifties, 10 twenties, 2 tens, and 16 fives; $700