4.2 Integer, Coin and Stamp Problems

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Presentation transcript:

4.2 Integer, Coin and Stamp Problems Hubarth Math 90

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

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

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

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