Question 100777: ten years from now, sofia will be three times as old as she was eight years ago. how old is sofia now?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Problems such as this are confusing unless you pick them apart and start looking at how to
write each term. Since you are asked to find Sophia's present age, that means you don't know
her present age. S let's start by representing her present age by the letter S.
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How old was she 8 years ago? That would be found by subtracting 8 from her present age. So
we could say that 8 years ago Sophia was S - 8 years old.
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How old will she be in 10 years? That would be found by adding 10 to her present age. So
we could say that in 10 years Sophia will be S + 10 years old.
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So now we have three different ages for Sophia ... S - 8, S, and S + 10
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The problem now tells you that in 10 years from the present, Sophia will be 3 times as
old as she was 8 years ago. That means that if we multiplied her age at 8 years ago by 3
we should get her age at 10 years from now. This translates to "3 times her age at S - 8
should equal her age at S + 10. In equation form we can write this as:
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3(S - 8) = S + 10
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Do the distributed multiplication on the left side of this equation by multiplying
3 times each of the terms inside the parentheses. This results in:
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3S - 24 = S + 10
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Get rid of the -24 on the left side by adding 24 to both sides, and this addition changes
the equation to:
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3S = S + 34
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Next, get rid of the S on the right side by subtracting S from both sides to get:
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2S = 34
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Finally, solve for S by dividing both sides by 2 which is the multiplier of S to give you
the answer of:
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S = 34/2 = 17
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Since S represents Sophia's present age, we can say that Sophia is now 17 years old.
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Let's check our answer. If Sophia is presently 17 years old, then 8 years ago she was 9
(or 17 - 8 - 9) and 10 years from now she will be 17 + 10 = 27. Is 27 three times 9?
Yes it is, so we have found that in 10 years she will be 3 times the age that she was
8 years ago. Our answer checks!
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Sophia is presently 17 years old.
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Hope this helps you to see your way through the confusion of the problem.
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