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Let 'x' be the age of Carol's brother at present 'y' be the age of Carol at present Two years from now: 'x+2' --age of Carol's brother 'y+2' ---Carol's age ----------------------------------- -Carol is 5 times as old as her brother y = 5x ------equation 1 ---------------------------------- -she will be three times as old as her brother in two years (y+2) = 3(x+2) y + 2 = 3x + 6 y = 3x + 6 - 2 y = 3x + 4 -----equation 2 ----------------------------------- Substitute equation 1 to equation 2 y = 3x + 4 5x = 3x + 4 5x - 3x = 4 2x = 4 x = 2 ---------------------------------- Substitute x=2 to equation 1 y = 5x y = 5(2) y = 10 --------------------------------- Therefore Carol is 10 years old and her brother is 2 years old.