Question

Lilly and Rosie are sisters. The sum of their ages is 19 and the positive difference of their ages is 9. Set up a system of equations involving Lilly’s age, L, and Rosie’s age, R, assuming that Lilly is the older child. Solve the system to find their ages.

Answer 1

14

Explanation:

The sum of their age is 19.

This means that when you add their ages together, it will be 19.

L+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+R=19.

Solve for L.

Subtract R on both sides.

L=19-R

Now use the substitution method (replacing or "substituting" L with 19-R) for the next equation.

L-R=9

(19-R)-R=9

19-2R=9

-2R=-10

R=5

Rosie's age is 5.

Rosie's age is 5. Now use the first equation to find Lily's age.

L+5=19

L=14.

Lily's age is 14.