Question 1165625
m represents mark's age and s represents sarah's age.


the sum of their ages is 102, therefore:
m + s = 102


11 years ago, mark was 3 times sarah's age, therefore:
m - 11 = 3 * (s - 11)


solve for m in the first equation to get:
m = 102 - s.


replace m with 102 - s in the second equation to get:
m - 11 = 3 * (s - 11) becomes:
102 - s - 11 = 3 * (s - 11).
simplify to get:
102 - s - 11 = 3 * s - 33.
add s to both sides of the equation andeadd 33 to both sides of the equation to get:
102  - 11 + 33 = 4 * s
simplify to get:
124 = 4 * s.
solve for s to get:
s = 124 / 4 = 31.


since m + s = 124 and s = 31, then m = 124 - 31 = 71
you have:
m = 71
s = 34


m + s = 102
m - 11 = 3 * (s - 11) becomes:
71 - 11 = 3 * (31 - 12) which becomes;
60 = 3 * 20 which is true.


the requirements of the problem are satisfied.
the solution is that mark is 71 years old now.
additional information is that sarah is 31 years old now.