SOLUTION: Lily and Rosie are sisters. The sum of their age is 19 and the positive difference if their age is 9. Set up a system of equations involving Lily's age, L, and Rosie's age, R, assu

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: Lily and Rosie are sisters. The sum of their age is 19 and the positive difference if their age is 9. Set up a system of equations involving Lily's age, L, and Rosie's age, R, assu      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 970302: Lily and Rosie are sisters. The sum of their age is 19 and the positive difference if their age is 9. Set up a system of equations involving Lily's age, L, and Rosie's age, R, assuming Lily is the older child. Solve the system to find the ages
Answer by erica65404(394) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of their age is 19.

This means that when you add their ages together, it will be 19.
L+%2B+R+=+19

The positive difference of their age is 9.


It tells you that Lily is the older child.
Since the difference is a positive number, that means it would be Lily's age minus Rosie's age since Lily is older.
L+-+R+=+9
Now you have 2 equations that can be used to find their ages.

Start with the first equation
L%2BR=19
solve for L
L%2BR=19
L%2BR-R=19-R
L=19-R
Now use the substitution method (replacing or "substituting" L with 19-R) for the next equation.
L-R=9
%2819-R%29-R=9
19-2R=9
19-19-2R=9-19
-2R=-10
%28-2%29R%2F-2+=+%28-10%29%2F-2
R=5
Rosie's age is 5. Now use the first equation to find Lily's age.
L%2BR=19
L%2B5=19
L%2B5-5=19-5
L=14
Lily's age is 14.


-----------------------------------------
If you have questions, email me at ericahigley@yahoo.com