Question

Of two numbers ,3 times the larger one is greater than 4 times the smaller one by 7.Also, the sum of numbers is larger than 6 times their difference by 4.Find the numbers.

Answer 1

Let the greater one be x and smaller one be y. So :-

3x - 4y =7
3x-4y-7=0 .. .....(1)

(x + y) - 6(x - y) = 4

x + y -6x + 6y = 4

-5x + 7y = 4 ....(2)

Now by substitution method :-

From equation (2)

7y = 4+ 5x

y = (4 + 5x) / 7 .... (3)

Now by putting this value of y in equation (1) :-

3x - 4{(4+ 5x) / 7} = 6

21x -16 - 20x = 42

x = 58

Therefore, by putting this value of x in equation (3) , value of y will be ;-

y = {4 + 5(58)} / 7

= (4 + 290) / 7

= 294 / 7

= 42

Coclusion :-

Bigger no. (x) = 58

Smaller no. (y) = 42