Question 909834
Let x be the smaller number and (76 – x) will be the larger.
x + (76-x) = 76
x/8 + (76-x)/11 = 8
11x/88 + 8(76-x)/88 = 8
11x + 608-8x = 704
11x – 8x = 704-608
3x = 96
X = 32
76-x = ?
76 – 32 = 44

The smaller number is 32 and the larger number is 44.

Checking:
X + (76-x) = 76
32 + (76-32) = 76
32 + 44 = 76

x/8 + (76-x)/11 = 8
32/8 + (76-32)/11 = 8
4 + 44/11 = 8
4 + 4 = 8