 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
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

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

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.