Question 341326: John is 13 years less than 3 times as old as his son. Six years ago, he was 14 years more than twice as old as his son was then. How old is John?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! John is 13 years less than 3 times as old as his son.
Six years ago, he was 14 years more than twice as old as his son was then.
How old is John?
:
Let j = John's present age
Let s = son's present age
:
Write a equation for each statement:
:
"John is 13 years less than 3 times as old as his son."
j = 3s - 13
;
" Six years ago, he was 14 years more than twice as old as his son was then."
j - 6 = 2(s-6) + 14
j - 6 = 2s - 12 + 14
j - 6 = 2s + 2
j = 2s + 2 + 6
j = 2s + 8
:
Replace j with (3s-13) from the 1st statement:
3s - 13 = 2s + 8
3s - 2s = 8 + 13
s = 21 yrs is the son's age
:
How old is John? j = 3s - 13
j = 3(21) - 13
j = 63 - 13
j = 50 yrs is John's age
:
:
Check solutions in the statement:
"Six years ago, he was 14 years more than twice as old as his son was then. "
50 - 6 = 2(21 - 6) + 14
44 = 2(15) + 14; confirms our solution
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