Jawaban:

Let's start by assigning variables to represent the number of goldfish and angelfish in the pet shop. Let x be the common multiple between 5 and 6, and let 5k and 6k be the initial numbers of goldfish and angelfish, respectively.

So, we have:

- Number of goldfish = 5k

- Number of angelfish = 6k

- x = LCM(5, 6) = 30

After 30 goldfish were sold, the new number of goldfish is (5k - 30), and the number of angelfish remains the same (6k). The ratio of goldfish to angelfish is now 1:2, so we can write:

(5k - 30)/(6k) = 1/2

To solve for k, we can cross-multiply and simplify:

10k - 60 = 6k

4k = 60

k = 15

Therefore, the initial number of goldfish and angelfish were:

- Number of goldfish = 5k = 5(15) = 75

- Number of angelfish = 6k = 6(15) = 90

So, there were 75 + 90 = 165 goldfish and angelfish altogether in the shop at first.