document.write( "Question 1120930: A man has two daughters, one three times as old as the other. The man is five times as old as his older daughter and in 5 years he will be five times as old as the younger. Find their present ages. \n" ); document.write( "

Algebra.Com's Answer #736637 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The solution by the other tutor is fine. However, I would define my variables differently to avoid having to work with fractions, since it's always more likely to make mistakes calculating with fractions than with whole numbers.

\n" ); document.write( "So let the younger daughter's age be x; then the older daughter's age is 3x; and then the father's age is 15x.

\n" ); document.write( "The father 5 years from now will be 5 times as old as his younger daughter:

\n" ); document.write( " $\"15x%2B5+=+5%28x%2B5%29\"$
\n" ); document.write( " $\"15x%2B5+=+5x%2B25\"$
\n" ); document.write( " $\"10x+=+20\"$
\n" ); document.write( " $\"x+=+2\"$

\n" ); document.write( "The younger daughter is x=2; the older daughter is 3x=6; the father is 15x=30.

\n" ); document.write( "Note that, if a formal algebraic solution is not required, the problem can be solved quickly with a bit of logical reasoning.

\n" ); document.write( "Since the older daughter is 3 times as old as the younger daughter and the father is 5 times as old as his older daughter, the man is 15 times as old as his younger daughter.

\n" ); document.write( "Since ages (in age problems like this!) must be whole numbers, the possibilities for the ages of the younger daughter and the father are 1 and 15, or 2 and 30, or 3 and 45, or ....

\n" ); document.write( "Common sense tells us that 2 and 30 is by far the most likely combination; a bit of checking shows us that it satisfies all the conditions of the problem. \n" ); document.write( "

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