Question

Find two consecutive odd numbers such that the sum of three-sevenths of the first number and one-third of the second number is equal to thirty-eight.. A) 29 and 31. B) 39 and 41. C) 49 and 51

Answer 1

x = 1st number
x + 2 = 2nd number

3/7x + 1/3(x + 2) = 38
3/7x + 1/3x + 2/3 = 38
3/7x + 1/3x = 38 - 2/3
9/21x + 7/21x = 114/3 - 2/3
16/21x = 112/3
x = 112/3 * 21/16
x = 2352/48
x = 49 <== 1st number

x + 2 = 49 + 2 = 51 <== 2nd number

Answer 2

(3/7) x + (1/3) (x + 2) = 38 

Multiply both sides by 21: 
21*(3/7) x + 21*(1/3) (x + 2) = 21*38 
9x + 7 (x + 2) = 798 
9x + 7x + 14 = 798 
16x = 784 
x = 49 

x + 2 = 51 so the are 49 and 51