Question

The sum of four consecutive odd integers is three more than five times the least of the integers. Find the integers.

Answer 1

Answer:

             9, 11, 13, 15

Step-by-step explanation:

{k - some integer}

2k+1  - the first odd integer (the least)

5(2k+1)  - five times the least

5(2k+1)+3 - three more than five times the least

2k+1+2 = 2k+3  - the odd integer consecutive to 2k+1

2k+3+2 = 2k+5  - the next odd consecutive integer (third)

2k+5+2 = 2k+7  - the last odd consecutive integer (fourth)

2k+1+2k+3+2k+5+2k+7 - the sum of four odd consecutive integers

2k+1 + 2k+3 + 2k+5 + 2k+7 = 5(2k+1) + 3

8k + 16 = 10k + 5 + 3

     - 10k       -10k

-2k + 16 = 8

     -16       - 16    

      -2k = -8  

    ÷(-2)    ÷(-2)  

      k = 4

2k+1 = 2•4+1 = 9

2k+3 = 2•4+3 = 11

2k+5 = 2•4+5 = 13

2k+7 = 2•4+7 = 15  

Check: 9+11+13+15 = 48;  48-3 = 45;  45:5 = 9 = 2k+1