SOLUTION: At a certain point in his life (time 3), Arnold had an age with the second digit being three and with the square of the first digit being his actual age reversed. Earlier in his li
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Question 711390: At a certain point in his life (time 3), Arnold had an age with the second digit being three and with the square of the first digit being his actual age reversed. Earlier in his life, (time 2) Arnold had a father who was twice as old as he was. Twenty five years prior to that (time 1) the ratio of Arnold’s age to his father’s age was one to three.
Your tasks are to determine how old Arnold was at each of the 3 times identified in the problem:
time 1,
time 2, and
time 3.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
At a certain point in his life (time 3), Arnold had an age with the second digit being three and with the square of the first digit being his actual age reversed.
a = the 1st digit
10a+3 = his age in time 3
a^2 = 30+a
a^2 - a - 30 = 0
(a-6)(a+5) = 0
the positive solution
a = 6
Therefore:
63 = age in time 3
:
Earlier in his life, (time 2) Arnold had a father who was twice as old as he was.
Earlier in life: F = 2A
:
Twenty five years prior to that (time 1) the ratio of Arnold’s age to his father’s age was one to three.
=
Cross multiply
F-25 = 3(A-25)
F - 25 = 3A - 75
Replace F with 2A
2A - 25 = 3A - 75
-25 + 75 = 3A - 2A
50 = A
Arnold is 50 yrs old and Dad was 100 in time 2
:
=
A is 25 yrs old and Dad is 75 yrs old in time 1
Your tasks are to determine how old Arnold was at each of the 3 times identified in the problem:
time 1, 25
time 2, 50
time 3, 63
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