To solve for y in the equation 1 + 2 + (3/10)y = (8/15)y + 0.78, we need to first combine like terms.

1 + 2 = 3

Therefore, the equation becomes:

3 + (3/10)y = (8/15)y + 0.78

Next, we need to get rid of the fractions by multiplying every term by the least common multiple of the denominators, which is 30:

30(3) + 30(3/10)y = 30(8/15)y + 30(0.78)

Expanding and simplifying:

90 + 9y = 16y + 23.4

Now, we want to isolate the variable y. Let's start by moving all terms with y to one side of the equation:

9y - 16y = 23.4 - 90

-7y = -66.6

Dividing by -7 to solve for y:

y = 9.5142857

Therefore, the solution to the equation is y ≈ 9.514.