<span>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</span>
