document.write( "Question 100777: ten years from now, sofia will be three times as old as she was eight years ago. how old is sofia now? \n" ); document.write( "
Algebra.Com's Answer #73389 by bucky(2189)\"\" \"About 
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
\n" ); document.write( "write each term. Since you are asked to find Sophia's present age, that means you don't know
\n" ); document.write( "her present age. S let's start by representing her present age by the letter S.
\n" ); document.write( ".
\n" ); document.write( "How old was she 8 years ago? That would be found by subtracting 8 from her present age. So
\n" ); document.write( "we could say that 8 years ago Sophia was S - 8 years old.
\n" ); document.write( ".
\n" ); document.write( "How old will she be in 10 years? That would be found by adding 10 to her present age. So
\n" ); document.write( "we could say that in 10 years Sophia will be S + 10 years old.
\n" ); document.write( ".
\n" ); document.write( "So now we have three different ages for Sophia ... S - 8, S, and S + 10
\n" ); document.write( ".
\n" ); document.write( "The problem now tells you that in 10 years from the present, Sophia will be 3 times as
\n" ); document.write( "old as she was 8 years ago. That means that if we multiplied her age at 8 years ago by 3
\n" ); document.write( "we should get her age at 10 years from now. This translates to \"3 times her age at S - 8
\n" ); document.write( "should equal her age at S + 10. In equation form we can write this as:
\n" ); document.write( ".
\n" ); document.write( "3(S - 8) = S + 10
\n" ); document.write( ".
\n" ); document.write( "Do the distributed multiplication on the left side of this equation by multiplying
\n" ); document.write( "3 times each of the terms inside the parentheses. This results in:
\n" ); document.write( ".
\n" ); document.write( "3S - 24 = S + 10
\n" ); document.write( ".
\n" ); document.write( "Get rid of the -24 on the left side by adding 24 to both sides, and this addition changes
\n" ); document.write( "the equation to:
\n" ); document.write( ".
\n" ); document.write( "3S = S + 34
\n" ); document.write( ".
\n" ); document.write( "Next, get rid of the S on the right side by subtracting S from both sides to get:
\n" ); document.write( ".
\n" ); document.write( "2S = 34
\n" ); document.write( ".
\n" ); document.write( "Finally, solve for S by dividing both sides by 2 which is the multiplier of S to give you
\n" ); document.write( "the answer of:
\n" ); document.write( ".
\n" ); document.write( "S = 34/2 = 17
\n" ); document.write( ".
\n" ); document.write( "Since S represents Sophia's present age, we can say that Sophia is now 17 years old.
\n" ); document.write( ".
\n" ); document.write( "Let's check our answer. If Sophia is presently 17 years old, then 8 years ago she was 9
\n" ); document.write( "(or 17 - 8 - 9) and 10 years from now she will be 17 + 10 = 27. Is 27 three times 9?
\n" ); document.write( "Yes it is, so we have found that in 10 years she will be 3 times the age that she was
\n" ); document.write( "8 years ago. Our answer checks!
\n" ); document.write( ".
\n" ); document.write( "Sophia is presently 17 years old.
\n" ); document.write( ".
\n" ); document.write( "Hope this helps you to see your way through the confusion of the problem.
\n" ); document.write( ". \n" ); document.write( "
\n" );