SOLUTION: Mark's age next year will be three times as old as Kim's age two years ago. If their present ages add to 21, how old is each now?

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M + K = 21
so
M = 21-K
.
Mark's age next year: M+1
Kim's age 2 years ago: K-2
M+1 = 3*(K-2)
.
Substitute M = 21-K.
.
21-K +1 = 3K -6
28 = 4K
K = 7
.
M = 21-7
M = 14
.
Check.
M+1 =15
3(K-2) = 15
Correct.
.
Answer: Mark is 14, and Kim is 7.
.
Done.