Question 276487
Hannah, Mark and Tom have a combined age of 68.
h + m + t = 68 
:
Hannah is twice as old as the difference between Mark and Tom's age.
h = 2(m - t)
:
 Mark and Tom's combined age is 16 times Hannah's age.
m + t = 16h
-16h + m + t = 0
:
Subtract the above equation from the 1st equation
h + m + t = 68
-16h + m + t = 0
-------------------subtraction eliminates m & t, find h
17h = 68
h = {{{68/17}}}
h = 4 yrs is Hannah's age
:
Replace h with 4 in the equation m + t = 16h
m + t = 16(4)
m + t = 64
:

Replace h in the equation h = 2(m-t)
2(m - t) = 4
Simplify, divide by 2
m - t = 2
;
Add the two equation
m + t = 64
m - t = 2
-------------
2m = 66
m = 33 yrs is Marks age
then
31 is Tom's age
:
:
Check total
4 + 33 + 31 = 68