The sum of two numbers is 48. if one third of one number is 5 greater than one sixth of another number, which of the following is the smaller number? a. 6 b. 26 c. 22 d. 42

The sum of two numbers is 48.
a + b = 48
;
If one third of one number is 5 greater than one sixth of another number,
a = b + 5
multiply both sides by 6, cancel the fractions
2a = b + 30
2a - b = 30
use elimination to solve this
a + b = 48
2a - b =30
Addition eliminates b, find a
3a = 78
a = 
a = 26
then
26 + b = 48
b = 48 - 26

b = 22