Question 616605
First, let x=Mike's age because we do not know what it is.


David= x + 5


Sheila is one year older than David so add one to David's age and so forth:


Sheila= x + 6

Nancy = x + 9

Claire = x + 10


Now we know that all of their ages added together equal 120 years. So, we add all of the equations together and put them equal to 120.


(x + 10) + (x + 9) + (x + 6) + (x + 5) + x = 120


Add all like terms


5x + 30 = 120


Subtract 30 from both sides to get the x variable by itself.


5x = 120 - 30
5x = 90


Now divide both sides by 5 to get x by itself.


5x/5 = 90/5
x = 18


x = Mike's age so Mike is 18. Now substitute 18 in the above equations to get each age.


Mike = 18 years old
David = 18 + 5 = 23 years old
Sheila = 18 + 6 = 24 years old
Nancy = 18 + 9 = 27 years old
Claire = 18 + 10 = 28 years old


Now add each age and they will equal 120 years.


18 + 23 + 24 + 27 + 28 = 120
120 = 120