SOLUTION: Adam's father is 19 times as old as Adam. Adam's grandfather's age is 14 years less than twice Adam's fathers age. The sum of all their ages is 102. How old are each of the th

Question 1099565: Adam's father is 19 times as old as Adam. Adam's grandfather's age
is 14 years less than twice Adam's fathers age. The sum of all their
ages is 102. How old are each of the three persons?
Found 3 solutions by Fombitz, Edwin McCravy, ikleyn:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
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Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!

Adam's father is 19 times as old as Adam. F = 19A Adam's grandfather's age is 14 years less than twice Adam's fathers age. G = 2F - 14 The sum of all their ages is 102. A + F + G = 102 Solve the system: Substitute (19A) for F in G = 2F - 14 G = 2(19A) - 14 G = 38A - 14 Substitute (19A) for F and (38A-14) for G in A + F + G = 102 A + (19A) + (38A-14) = 102 A + 19A + 38A - 14 = 102 58A - 14 = 102 58A = 116 A = 2 Substitute 2 for A in F = 19A F = 19(2) F = 38 Substitute (38) for F in G = 2F - 14 G = 2(38) - 14 G = 76-14 G = 62 Edwin

Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Adam's father is 19 times as old as Adam. Adam's grandfather's age
is 14 years less than twice Adam's fathers age.
The sum of all their ages is 102. How old are each of the three persons?
~~~~~~~~~~~~~~~~~~~~~

Adam + Father + Grandfather = 102. A + 19A + 2*(19A)-14 = 102. A + 19A + 38A - 14 = 102 ====> 58A = 102 + 14 = 116 ====> A = = 2. Answer. Adam is 2 years old; his father is 19*2 = 38 years old and the grandfather is 2*38-14 = 62 years old.

Why I wrote this solution ?

For only one simple reason. This problem is for ONE UNKNOWN and it is designed for 5-6 grade students, who know NOTHING about systems of equations. Therefore, my goal was to present an ADEQUATE solution as SIMPLE as possible (and as it SHOULD be).

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