# 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.