SOLUTION: when the son will be as old as his father today, the sum of their ages will be 126.when the father was as old as his son today, the sum of their ages then was 38.Find their presen
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Question 953752: when the son will be as old as his father today, the sum of their ages will be 126.when the father was as old as his son today, the sum of their ages then was 38.Find their present ages
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when the son will be as old as his father today, the sum of their ages will be 126.when the father was as old as his son today, the sum of their ages then was 38.Find their present ages
Find their present ages
:
let f = father's age
let s = son's age
let d = f - s, their age difference
:
"when the son will be as old as his father today, the sum of their ages will be 126."
(s+d) + (f+d) = 126
s + f + 2d = 126
replace d with (f-s)
s + f + 2(f-s) = 126
s + f + 2f - 2s = 126
3f - s = 126
:
"when the father was as old as his son today, the sum of their ages then was 38."
(f-d) + (s-d) = 38
s + f - 2d = 38
replace d with (f-s)
s + f - 2(f-s) = 38
s + f - 2f + 2s = 38
-f + 3s = 38
:
Use elimination here, multiply the above equation by 3, add to the 1st eq
-3f + 9s = 114
+3f - s = 126
---------------Adding eliminates f, find s
8s = 230
s = 240/8
s = 30 yrs is the son's age
Find Dad's age using equation 3f -s = 126
3f -30 = 126
3f = 126 + 30
3f = 156
f = 156/3
f = 52 yrs is Father's age
:
:
Confirm this in the statement (there is a 22 yr difference in age):
when the son will be as old as his father today, the sum of their ages will be 126."
30 + 22 + 52 + 22 = 126
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