Question 1165625: The sum of the ages of mark and Sarah is 102 years. 11 years ago mark was 3 times Sarah’s age. How old is mark now? Found 2 solutions by Theo, MathTherapy:Answer by Theo(13342) (Show Source): You can put this solution on YOUR website! 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.
Let Mark's age be M
Then Sarah's is: 102 - M
We then get: M - 11 = 3(102 - M - 11)
M - 11 = 3(91 - M)
M - 11 = 273 - 3M
M + 3M = 273 + 11
4M = 284
Mark, or