A girl is 5 years younger than her sister and the product of their ages is 204. How old is the older sister?

Question

Hi, I need help with the question in the title.

Answer 1

Alex,

 

G = age of girl

S = age of her sister

 

G = S-5

GS = 204

 

Using substitution

(S-5)(S) = 204

S²-5S = 204

and

S² - 5S  - 204 = 0

 

Now we can factor and solve for S.

 

(S+12)(S-17) = 0

S = -12, 17

 

But negative numbers are not possible so S = 17

The sister is 17.