Solve by using a system of two equations in two variables. 27) A father, being a

Question

Solve by using a system of two equations in two variables.
27) A father, being asked his age and that of his son, said,"If you add 4 to my age and divide the sum by 4, you will have myson's age. But 6 years ago i was 7.5 times as old as my son." Findtheir ages.
Thank you! Please use an equation.
27) A father, being asked his age and that of his son, said,"If you add 4 to my age and divide the sum by 4, you will have myson's age. But 6 years ago i was 7.5 times as old as my son." Findtheir ages.
Thank you! Please use an equation.

Explanation / Answer

Let the father's age be x and the son's age be y If you add 4 to the father's age and divide by 4, you get theson's present age (x+4)/4 = y => x + 4 = 4y => x = 4y - 4  (1) Six years ago the father was 7.5 times as old as the son was 6years ago (x-6) = 7.5(y-6) => x-6 = 7.5y - 45 => x = 7.5y -39   (2) Equating (1) and (2) 4y - 4 = 7.5y - 39 Hence, y = 10 x = 36

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