NUMBER PROBLEMS

1.   The larger of two numbers is 2 more than the smaller.  Their sum is 18.  Find the number.

   Larger = x+2                              x+x+2 = 18                                                  8

   Smaller = x                                  2x + 2 = 18

                                                          2x = 16

                                                          x = 8

2.   The larger of two numbers is three times the smaller.  Twice the larger decreased by the smaller is 10.  Find the numbers.

   Large = 3x                                   2(3x) - x = 10                                                2

   Smaller = x                                  6x - x = 10

                                                          5x = 10

                                                          x = 2

3.   The sum of three consecutive numbers is 18.  Find the numbers.

   1st = x                                          3x + 3 = 18                                                   5,6,7

   2nd = x+1                                               3x = 15

   3rd = x+2                                                x = 5

4.   The sum of two even consecutive numbers is 34.  Find the numbers.

   1st = x                                          2x + 2 = 34                                                   16,18

   2nd = x+2                                               2x = 32

                                                          x = 16

5.   The sum of three odd consecutive numbers is 39.  Find the numbers.

   1st = x                                          x+x+2+x+4 = 39                                       11,13,15

   2nd = x+2                                               3x + 6= 39

   3rd = x+4                                                3x = 33

                                                          x = 11

6.   The sum of three numbers is 30.  The second exceeds the first by three.  The third number is 6 more than the first.  Find the numbers.

   1st = x                                          x+x+3+x+6 = 30                                       7,10,13

   2nd = x+3                                               3x + 9 = 30

   3rd = x+6                                                3x = 21

                                                          x = 7

7.   The sum of the first and third odd integers exceeds the second by 5.  Find the numbers.

   1st = x                                          x+x+4 = x+2+5                                         3,5,7

   2nd = x+2                                               2x + 4 = x + 7

   3rd = x+4                                                x + 4 = 7

                                                          x = 3

8.   What number increased by one third of itself is 12?

Number = x                                                x + 1/3 x = 12                                              9

                                                          4/3 x = 12

x = 9