Question 713383
Let

P = Patrick's age

M = Mother's age



"If you add five to the sum of Patrick's age and his mother's age, the total is 48", so we know that 5+P+M = 48


5+P+M = 48


P+M = 48-5


P+M = 43


M = 43-P


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"Patrick's mother is five years less than three times the age of Patrick", so we also know that


M = 3P - 5


43 - P = 3P - 5 ... plug in M = 43 - P


I'll let you finish up. You would solve this last equation for P. Once you have P, you can find M.