document.write( "Question 719135: Rena is 6 years older than her younger sister. After 1 0 years, the sum of their ages will be 50 years. Find their present ages.
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Algebra.Com's Answer #441241 by jsmallt9(3758) $\"\"$ $\"About$

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Before we start, two suggestions that can help with this and other similar problems:

When deciding what your variable will represent, try to choose a lower number. Then the bigger numbers will be the variable plus something and/or times something. Addition and multiplication are easier to work with. (If you make the variable represent a large number, then you will use subtraction and/or division to express the smaller numbers.
In these age problems, they usually talk about multiple people and multiple time periods (now, in the past and.o in the future). Try find an expression for each person for each time period before you start trying to solve the problem.

In this problem we have two people and two time periods (now and 10 years from now). So we are going to find four expressions: Rena's age now, her age in 10 years, the sister's age now and her age in 10 years. Of these four ages, the lowest is the sister's age now. So that is what we will represent with our variable:
\n" ); document.write( "Let y = younger sister's age now.
\n" ); document.write( "Since Rena is 6 years older, her current age would be: y + 6
\n" ); document.write( "In 10 years, both of them will be 10 years older. So the sisters age in 10 years will be her current age, y, plus 10: y + 10. And Rena's age in 10 years will be her current age, y + 6, plus 10: (y + 6) + 10 or y + 16.
\n" ); document.write( "It can help to put these expressions in a table format:
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document.write( "          Age now      Age in 10 years\r\n" );
document.write( "Rena       y + 6           y + 16\r\n" );
document.write( "Sister       y             y + 10\r\n" );
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\n" ); document.write( "Now that we have expressions for Rena and her sister's ages now and in 10 years we can start to solve the problem. We are told that the sum (addition) of their ages in 10 years will be 50. So:
\n" ); document.write( "Rena's age in 10 years + her sister's age in 10 years = 60
\n" ); document.write( "Using our expressions this becomes:
\n" ); document.write( "(y + 16) + (y + 10) = 50
\n" ); document.write( "Now we solve. First we simplify:
\n" ); document.write( "2y + 26 = 50
\n" ); document.write( "Subtract 26:
\n" ); document.write( "2y = 24
\n" ); document.write( "Divide by 2:
\n" ); document.write( "y = 12

\n" ); document.write( "Looking back to the table or \"Let y = younger sister's age now\", we can understand that Rena's sister's current age is 12 years old. Looking back we can also see that the expression for Rena's current age is y + 6. Since y = 12, Rena's current age would be 12 + 6 or 18 years old. \n" ); document.write( "

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