Mrs. Napholtz's Math Site

Coin Problems

Tickets to the school play cost $3.00 for adults and $2.00 for students. If 200 people attended the performance, and the receipts totaled $450, how many students saw the play?

Total number of tickets: a + s = 200

Total money: 3a + 2s = 450

Multiplty the top equation by -2:

-2a - 2s = -400

3a + 2s = 450

Add these equations:

a = 50

s = 150

ANS: 50 adults and 150 students.

Pam has some nickels, dimes, and quarters worth $6.75. There are four times as many nickels as dimes, and five more quarters than dimes. How many of each kind of coin does she have?

Number | Value | Total Value | |

Nickel | 4d | 5 | 20d |

Dime | d | 10 | 10d |

Quarter | d + 5 | 25 | 25d + 125 |

The total amount of money is $6.75.

20d + 10d + 25d + 125 = 675

55d + 125 = 675

55d = 550

d = 10

Answer: 40 nickels, 10 dimes, 15 quarters.

Jeremy has 24 quarters and half dollars. If he had twice as many half dollars and half as many quarters, he would have $2 more. How much money does he have?

ACTUAL | "IF" | |||||
---|---|---|---|---|---|---|

Number | Value | Total Value | Number | Value | Total Value | |

Quarters | n | 25 | 25n | n/2 | 25 | 25n/2 |

Half $$ | 24 - n | 50 | 1200 - 50n | 48 - 2n | 50 | 2400 - 100n |

Note: For the "IF" column, there are half the number of quarters and twice as many half dollars.

Fact for Equation: "IF" amount is $2.00 (200 cents!) more than the "Actual" amount.

25n/2 + 2400 - 100n = 25n + 1200 - 50n + 200

12.5n + 2400 - 100n = -25n + 1400

-87.5n + 2400 = -25n + 1400

-62.5n + 2400 = 1400

-62.5n = -1000

n = 16

Answer: He has 16 quarters and 8 half dollars.

He has $4.00 + $4.00

He has a total of $8.00

Tickets to the school volleyball game cost $1.00 for adults and $.75 for children. If 300 tickets were sold and the sales totaled $252.50, how many of each type were sold?

Number | Price | Total Cost | |

Adult | n | 1.00 | 1.00n |

Children | 300 - n | 0.75 | 225 - 0.75n |

The total price of all tickets is $252.50

1.00n + 225 - 0.75n = 252.50

0.25n + 225 = 252.50

0.25n = 27.50 7nbsp;&bnsp; Divide by 0.25.

n = 110

Answer: 110 Adult tickets and 190 Children tickets.

Janet has 5 fewer fifteen-cent stamps than twenty-cent stamps. If the total value of the stamps is $3.45, how many twenty-cent stamps does she have?

Number | Value | Total Value | |

Twenty Cent | n | 20 | 20n |

Fifteen Cent | n - 5 | 15 | 5n - 75 |

Since the total value of the stamps is 345 cents,

(Money from twenty cent stamps) + (Money from fifteen cent stamps) = 345

(20n) + (15n - 75) = 345

35n - 75 = 345

35n = 420

n = 12

n - 5 = 7

ANSWER: Janet has 12 twenty-cent stamps.

At a football game, 200 souvenirs were sold, some at $1.50 each and the rest of $2.50 each. If the proceeds from the sales totaled $380, how many of each kind were sold?

Number | Price | Total Price | |

Cheap ones | n | 1.50 | 1.50n |

Expensive ones | 200 - n | 2.50 | 2.50(200 - n) |

Since the total value of the sales is $380.00,

(Money from cheap souvenirs) + (Money from expensive souvenirs) = 380.00

(1.50n) + 2.50(200 - n) = 380.00 Distribute!

(1.50n) + (500 - 2.50n) = 380.00 Remember:1.50n - 2.50n = -1.00n

500 - 1.00n = 380.00 Subtract 500

-1.00n = -120 Divide by -1

n = 120

200 - n = 80

ANSWER: 120 souvenirs at $1.50, and 80 souvenirs at $2.50.

Jack has 4 more nickels than dimes, and the total value of the money is $1.25. How many nickels does he have?

Number | Value | Total Value | |

Nickels | d + 4 | 5 | 5d + 20 |

Dimes | d | 10 | 10d |

Since the total amount of money is 125 cents,

(Money from nickels) + (Money from dimes) = 125

(5d + 20) + 10d = 125

15d + 20 = 125

15d = 105

d = 7

d + 4 = 11

ANSWER: Jack has 11 nickels.

At a sandwich shop, sandwiches cost $1.50 each and fruit drinks cost $.40 each. If a bill for an order of 20 items was $17.00, how many fruit drinks were ordered?

Price | Number | Total Price | |

Sandwiches | 150 | n | 150n |

Fruit Drinks | 40 | 20 - n | 800 - 40n |

Since the total cost is $17.00, we get

150n + 800 - 40n = 1700

110n + 800 = 1700

110n = 900

n = 900/110

n is not a whole number!

Answer: Since a non-whole number of sandwiches cannot be sold, this problem has NO SOLUTION.

Amelio has 6 more nickels than dimes, and the total value is $2.10. how many nickels does he have?

Number | Value | Total | |

Nickels | n + 6 | 5 | 5n + 30 |

Dimes | n | 10 | 10n |

5n + 30 + 10n = 210

15n + 30 = 210

15n = 180

n = 12

Answer: Nickels = 12 + 6 = 18.