Question

Mr. and Mrs. Abuja weight x kg and y kg respectively. They both take a dieting course, at the end of which Mr. Ahuja loses 5 kg and weights as much as his wife weighed before the course. Mrs. Ahuja loses 4 kg and weighs ${\displaystyle \frac{7}{8}}$th of what her husband weighed before the course. Form two equations in x and y, find their weights before taking the dieting course.

Answer 1

Weight of Mr. Ahuja = x kg and weight of Mrs. Ahuja = y kg.
After the dieting,
x - 5 = y
x - y = 5                      ...(1)
and,
${\displaystyle y-4=\frac{7}{8}x}$
7x - 8y = - 32              ...(2)
Multiplying equation no. (1) by 7, we get
7x - 7y = 35                ....(3)

Now subtracting equation (2) from (3),
        7x - 7y = 35   
-      7x - 8y = - 32  
       -    +         +     
                y = 67
From (1)
x - 67 = 5
⇒ x = 72
Thus, weight of Mr. Ahuja = 72 kg and that of Mr. Anuja = 67 kg.