Question 315459
Ten years ago a father was seven times as old as his son,
 two years hence twice his age will be equal to five times his sons.
 what is the present age of son?
:
Write an equation for each statement, simplify:
"Ten years ago a father was seven times as old as his son,"
f - 10 = 7(s-10)
f - 10 = 7s - 70
f = 7s - 70 + 10
f = 7s - 60
:
"two years hence twice his age will be equal to five times his sons."
2(f + 2) = 5(s+2)
2f + 4 = 5s + 10
2f = 5s + 10 - 4
2f = 5s + 6
:
what is the present age of son?
Replace f with (7s-60) in the above equation:
2(7s - 60) = 5s + 6
14s - 120 = 5s + 6
14s = 5s + 6 + 120
14s - 5s = 126
9s = 126
s = {{{126/9}}}
s = 14 yrs, son's present age
:
:
Check solution, find father's age
f = 7s - 60
f = 7(14) - 60
f = 98 - 60
f = 38 yrs, father's age
:
"Ten years ago a father was seven times as old as his son, "
38 - 10 = 7(14-10)
28 = 7(4)
and
"two years hence twice his age will be equal to five times his sons."
2(38+2) = 5(14 + 2)
80 = 5(16); confirms our solution
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