1. 4.2 Integer, Coin and Stamp Problems
Hubarth
Math 90

2. Consecutive Integers are integers that follow on another in order.
What does this mean?
What are consecutive even integers?
What are consecutive odd integers?
Example 1
Find three consecutive even integers such that three times the second integer is 6 more
than the sum of the first and the third integer.
1𝑠𝑡=n
2𝑛𝑑=𝑛+2
3𝑟𝑑=𝑛+4
The three consecutive integers are: 4, 6, 8
3 𝑛+2 = 𝑛)+(𝑛+4 +6
3𝑛+6=2𝑛+10
𝑛=4

3. Coin and Stamp problem strategies- for each coin or stamp problems, write a numerical or
variable expression for the number of coins or stamps, the value of the coin/stamp in cents,
and the total value of the coins/stamps in cents. Use a table.
Example 2
A collection of stamps consist of 3¢ stamps and 8 ¢ stamps. The number of 8¢ stamps is five
more than three times the number of 3¢ stamps. The total value of all the stamps is $1.75.
Find the number of each type of stamps in the collection.
# of stamps
Value
Total Value 3¢ x 3 8¢
3𝑥+5 8 x = 3x
8(3x+5)
3𝑥+8 3𝑥+5 =175
3 5 +5=20
3𝑥+24𝑥+40=175
27𝑥+40=175
There are five 3 ¢ stamps and twenty 8 ¢ stamps.
27𝑥=135
𝑥=5

4. Example 3
A coin bank contains$1.20 in dimes and quarters. In all, there are nine coins in the bank.
Find the number of quarters in the bank.
𝑑𝑖𝑚𝑒𝑠=𝑛
𝑞𝑢𝑎𝑟𝑡𝑒𝑟𝑠=9−𝑛
# of coins
value
total value
dimes n 10
quarters
9-n 25
10n
25(9-n)
10𝑛+25 9−𝑛 =120
9−7=2
10𝑛+225−25𝑛=120
There are two quarters in the bank
−15𝑛=−105
𝑛=7

5. Practice
A coin bank contains nickels, dimes and quarters. There are five times as many nickels as dimes
and six more quarters than dimes. The total value of all coins is $6.30. Find the number of
each kind of coin in the bank.
𝑑𝑖𝑚𝑒𝑠=𝑑
𝑛𝑖𝑐𝑘𝑒𝑙𝑠=5𝑑
𝑞𝑢𝑎𝑟𝑡𝑒𝑟𝑠=𝑑+6
# of coins
Value
Total Value
dimes d 10
10d
nickels 5d 5
25d
quarters
d+6 25
25d+150
10𝑑+25𝑑+25𝑑+150=630
𝑑𝑖𝑚𝑒𝑠=8
𝑛𝑖𝑐𝑘𝑒𝑙𝑠=5 8 =40
𝑞𝑢𝑎𝑟𝑡𝑒𝑟𝑠=8+6=14
60𝑑+150=630
60𝑑=480
𝑑=8