Alocal fish market is selling fish and lobsters by the pound. the fish
costs $4.50 a pound, while the lobster costs $9.50 a pound. the fish
market sells 25.5 pounds and makes $189.75.

The local fish market sold 10.5 pounds of fish and 15 pounds of lobster

Given that local fish market is selling fish and lobsters by the pound

Let "F" be pounds of fish sold

Let "L" be the pounds of lobsters sold

Cost of one pound of fish = $ 4.50

Cost of one pound of losbter = $ 9.50

The fish  market sells 25.5 pounds and makes $189.75

We can frame a equation as:

pounds of fish sold + pounds of lobster sold = 25.5

F + L = 25.5 ------- eqn 1

The fish market makes $ 189.75

pounds of fish sold x Cost of one pound of fish + pounds of lobsters sold x Cost of one pound of losbter = 189.75

4.5F + 9.5L = 189.75 ----- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "F" and "L"

From eqn 1,

L = 25.5 - F ----- eqn 3

Substitute eqn 3 in eqn 2

4.5F + 9.5(25.5 - F) = 189.75

4.5F + 242.25 - 9.5F = 189.75

-5F = 189.75 - 242.25

-5F = -52.5

Substitute F = 10.5 in eqn 3

L = 25.5 - 10.5

Thus the pounds of fish sold is 10.5 and pounds of lobster is 15