Your mom bought a total of 15 shaddocks and watermelons and their total weight was 33.30 kg. If each shaddock weighed 1.8 kg and each watermelon weighed 2.5 kg, how many shaddocks and watermelons did your mom buy respectively?

Let's use S for the number of shaddocks and W for the number of watermelons.

S + W = 15

1.8S + 2.5W = 33.30

Let's solve S+W=15 for S.

S = 15 - W

Now we can use substitution to solve the system of equations. To do so, plug in 15-W for S in the second equation.

1.8 (15-W) + 2.5W = 33.30

Distribute and combine like terms.

27 - 1.8W + 2.5W = 33.30

0.7W + 27 = 33.3

0.7W = 6.3

W = 9

If there are 9 watermelons, then there are 15 - 9 = 6 shaddocks.

The answer is 6 shaddocks and 9 watermelons.