The sum of Emil's and Rosa's ages is 27 years. Nine years ago Emil was twice as old as Rosa was then. How old is each person? What are the two equations?

Let e = Emil's age and r = Rosa's age.

e + r = 27 since Emil's and Rosa's ages added together make a sum of 27 years.

(e - 9) = 2r - 9 since Emil's age minus 9 (9 years ago) is two times what Rosa's age is minus 9 (9 years ago)

Since you can't be twice someone's age for only 1 year, Emil is still twice Rosa's age.

So e + r = 27 and e = 2r.

Even though we don't know what 2r is, if we plug it in for e, we can find out.

2r + r = 27

This means 2r + 1r = 27.

Now you can simplify this to find each person's age.

3r = 27

27 / 3 = 9

r = 9

2r = 18

e = 2r = 18

e = 18

r = 9

So Emil is 18 years old and Rosa is 9 years old.