The local fish market sold 10.5 pounds of fish and 15 pounds of lobster
Solution:
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
F = 10.5
Substitute F = 10.5 in eqn 3
L = 25.5 - 10.5
L = 15
Thus the pounds of fish sold is 10.5 and pounds of lobster is 15