Question 284674
let the integers be x , x+1, x+2

3times the middle = 3(x+1)

5times the smaller =5x

7 times the largest = 7(x+2)

3(x+1)+5x=7(x+2)

3x+3+5x=7x+14

8x+3=7x+14

8x-7x=14-3

x=11

the numbers are 11 , 12, 13