MATHEMATICS · Multi-part · AoPS · Mathematics · Multi-Variable Linear Equations · Multi-Variable Linear Equations
Problem
A father is 24 years older than his son. Three years from now, the father’s age will be twice that of his son.
(i) Taking the present age of the son as x years and that of the father as y years, frame the two linear equations in x and y corresponding to the given conditions.
(ii) Construct a table of any two ordered pairs for each equation and plot both lines on the same graph paper, labelling the axes with appropriate units.
(iii) Determine the present ages of the father and the son by reading the coordinates of the intersection point of the two lines.
(iv) Using the same graph, estimate after how many years the father’s age will exceed his son’s age by exactly 18 years. (Hint: Represent the additional condition graphically and read the required point of intersection.)