SOLUTION: The sum of age of matt and Sam is 29,sam and Ben 26,ben and Matt 31,how old is the youngest?

Question 1095287: The sum of age of matt and Sam is 29,sam and Ben 26,ben and Matt 31,how old is the youngest?
Found 3 solutions by KMST, ikleyn, MathTherapy:
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
THE FIFTH GRADER'S SOLUTION:
The sum of the ages of the two oldest persons
must be greater than the other two sums including the youngest person.
So, Sam is the youngest.
If you switch from Sam to Matt in a pair,
the sum of ages increases by 37-26=11,
so Matt is 11 years older than Sam.
That means that the sum of ages for Matt and Sam (29)
is 11 more than twice Sam's age,
so 29-11=18 is twice Sam's age and Sam is .

ALGEBRA:
= Sam's age,
= Matt's age,
= Ben's age.
-->-->-->
-->-->-->-->-->

CONCLUSION: Algebra makes the statement shorter and requires no translation.
It is the easiest foreign language you will ever learn.
Answer by ikleyn(52930)   (Show Source): You can put this solution on YOUR website!
.

We are given M + S = 29, (1) S + B = 26, (2) B + M = 31. (3) Add all three equations (1), (2) and (3). You will get 2M + 2S + 2B = 29 + 26 + 31 = 86. Divide by 2 both sides of the last equation. You will get M + S + B = 43. (4) Now, subtract eq(1) from eq(4). You will get B = 43 - 29 = 14. ====> Ben is 14 years old. Next, subtract eq(2) from eq(4). You will get M = 43 - 26 = 17. ====> Matt is 17 years old. Finally, subtract eq(3) from eq(4). You will get S = 43 - 31 = 12. ====> Sam is 12 years old. Answer. Sam is the youngest, and he is 12 years old. Ben is 14 and Matt is 17 years old. Check. M + S = 17 + 12 = 29; S + B = 12 + 14 = 26; B + M = 14 + 17 = 31.

Solved.

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To see many other problems, solved by the similar method, look into the lesson
    - The tricks to solve some word problems with three and more unknowns using mental math
in this site.

Answer by MathTherapy(10558)   (Show Source): You can put this solution on YOUR website!
The sum of age of matt and Sam is 29,sam and Ben 26,ben and Matt 31,how old is the youngest?

The youngest is Sam, but , not 9.
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