Question 76252
Let larger number = x and smaller number = y.
Three times the larger number (= 3x) increased by 4 times the smaller = 3x + 4y.
This value is given 205.
So, 3x + 4y = 205 __________(1)


Six times the larger number (= 6x) plus 3 times the smaller = 6x + 3y.
This value is given 270.
So, 6x + 3y = 270 
or 2x + y = 90 ___________(2)

We now have to solve equations (1) and (2) to find x and y.
Multiplying both sides of eq (2) with 4 and subtracting both sides of eq (1) from it
4(2x + y) - (3x + 4y) = 4*90 - 205
(8x + 4y) - (3x + 4y) = 360 - 205
5x = 155
x = 31

So from (2)
2*31 + y = 90
or y = 90 - 62 = 28

Thus the numbers are 31 and 28.