SOLUTION: The sum of Kate's age and her mother's age is 52. Kate's mother is 20 yrs older than Kate. How old is each?

Question 653420: The sum of Kate's age and her mother's age is 52. Kate's mother is 20 yrs older than Kate. How old is each?
Answer by VirtualMathTutor(26) (Show Source): You can put this solution on YOUR website!
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.
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