Question

the sum of kate's age and her mother's age is 52. Kates mother is 20 years older than kate. how old is each

Answer 1

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.
Hope this helps!!1