SOLUTION: ___________10. The sum of Mario’s age and Luigi’s age is 80. Four years ago, Mario is thrice as old as Luigi. How old is Mario now?

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Question 1186453: ___________10. The sum of Mario’s age and Luigi’s age is 80. Four years ago, Mario is thrice as old as Luigi. How old is Mario now?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The solution from the other tutor is fine; I would set it up differently.

Given that Mario was 3 times as old as Luigi 4 years ago, I would do this:

Let x = Luigi's age 4 years ago
Then 3x = Mario's age 4 years ago

Given that the sum of their ages now is 80, do some simple mental arithmetic to determine that 4 years ago the sum of their ages was 72. Then

3x+x=72
4x=72
x=18

Their ages 4 years ago were
Luigi = x = 18
Mario = 3x = 54

ANSWER: Mario's age now is 54+4 = 58

Note setting the problem up that way leads to algebra that is simpler than in the solution from the other tutor.

And if formal algebra is not required, and/or if the speed of reaching a solution is important -- as in a timed math competition -- solving the problem by this method can be done mentally in far less time than with the formal method shown by the other tutor.