How old are John and Claire if twice John’s age plus five times Claire’s age is 204 and nine times John’s age minus three times Claire’s age is also 204?
1 Answer
Nov 11, 2014
Let the present of John is x years and Claire's age is y years.
as per the question, 2x + 5y = 204 ......... (a)
9x - 3y = 204 ........... (b)
equating (a) and (b)
9x - 3y = 2x + 5y
adding 3y to both sides,
9x -3y +3y = 2x + 5y +3y
9x = 2x + 8y
subtracting 2x from both sides,
9x -2x = 2x + 8y -2x
7x = 8y or x = (8y /7) ------(c)
substituting value of x in equation (a)
2 (8y/7) + 5y = 204
(16y / 7) + 5y = 204
16y + 35 y = (204) . (7)
51y = 1428
dividing both sides by 51 we get;
51y /51 = 1428 /51
y = 28
for x , substitute the value of x in equation (c)
x = 8y /7
x = (8. 28 ) / 7
x = 8.4 = 32.
