Question 653420
let Kate's age be K
Let Kate's mother's age be M


The sum of Kate age and her mother's age is 52, so

K + M = 52

Kate's mother is 20 years older then Kate, so

M = 20 + K

How old is each person?

Since M = 20 + K, substitute it into the first equation, that is, replace M with 20 + K

So, K + (20 + K) = 52

K + 20 + K = 52

2K + 20 = 52

Subtract 20 from both sides:

2K = 52 - 20

2K = 32

divide both sides by 2 to get

K = 16

Now we can find M, since M = 20 + K = 20 + 16 = 36

Kate is 16 years old and her mother is 36 years old.