SOLUTION: Josef’s father is seven time as old as he is. One year ago, he was nine times as old as Josef.Find Josef’s present age?

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Question 1167305: Josef’s father is seven time as old as he is. One year ago, he was nine times as old as Josef.Find Josef’s present age?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
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Josef’s father is seven times as old as he is. One year ago, he was nine times as old as Josef. Find Josef’s present age?
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f is k times as old as x. p years ago, f-p was v times as old as x-p.
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system%28f=kx%2Cf-p=v%28x-p%29%29
Findx.

kx-p=v%28x-p%29
kx-p=vx-vp
kx-vx=p-vp
x%28k-v%29=p-vp
highlight_green%28x=%28p-vp%29%2F%28k-v%29%29


system%28k=7%2Cp=1%2Cv=9%29
substitute.

x=%281-9%2A1%29%2F%287-9%29
x=%28-8%29%2F%28-2%29
highlight%28x=4%29

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x = Josef's age.


Then his father's age is 7x, according to the condition.


One year ago

    7x - 1 = 9*(x-1)


Simplify and solve

    7x - 1 = 9x - 9

    9 - 1 = 9x - 7x

      8   = 2x

      x   = 8/2 = 4.


ANSWER.  Josef is 4 years old now.

Solved.