Question 93718: In 3 years, Alex will be 3 times as old as his sister Precy. A year ago, Alex was 7 times as old as Precy.How old are they now? Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Let A be Alex's present age and P be Precy's present age.
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If A is Alex's present age, then a year ago he was A-1 years old. And a year ago Precy was
P -1 years old.
At that time Alex's age equaled 7 times Precy's age. So in equation form, a year ago:
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We can multiply out the right side to get:
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Then add +1 to both sides to get rid of the -1 on the left side and the equation becomes:
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Finally, subtract 7P from both sides and we get the standard form:
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This is our first equation. Remember it.
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If A is Alex's current age, then in 3 years his age will be A + 3. And if P is Precy's present
age, then in 3 years she will be P + 3. We are told that at that time Alex's age will be
3 times Precy's age. In equation form this is:
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Multiply our the right side and you have:
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Get rid of the 3 on the left side by subtracting 3 from both sides to get:
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And finally, put this equation in standard form by subtracting 3P from both sides to
get:
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So now we have a set of equations as follows:
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We can eliminate A by subtracting the two equations vertically in columns to get:
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This can be solved for P by dividing both sides by -4 to get that P (Precy's present age)
is +3.
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That means that a year ago Precy was 2 and at that time Alex was 7 times as old as she. Therefore,
a year ago Alex was 7*2 or 14 years old. But that was a year ago. That means that this
year Alex is a year older so he is currently 15.
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So we have that presently Alex is 15 and Precy is 3.
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Three years from now Alex will be 18 and Precy will be 6. So at that time Alex will be
3 times as old as Precy. That checks so it appears that our answer is correct.
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The answer is Alex is now 15 and Precy is now 3.
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Hope this helps you to see your way through this problem.
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