Alocal fish market is selling fish and lobsters by the pound. the fish costs $5.25 a pound, while the lobster costs $10.50 a pound. the fish market sells 28.5 pounds and makes $215.25

The fish market sells 12.5 pounds of lobster and 16 pounds of fish

Step-by-step explanation:

This exercise is solved by a system of equations, that is, a group of 2 (or more) linear equations. For that you must first determine your variables. In this case it is best to determine the following:

So, now you can build your system of equations.

You know that the fish market sells 28.5 pounds, this means that the sum of the fish sold and the lobster sold is 28.5 pounds. So: x+y=28.5 Equation (A)

On the other hand, the pound of fish is sold at $5.25 and the pound of lobster is sold at  410.5 and the fish market makes $215.25. This means that the sum between $5.25  multiplied by the pounds of fish sold and $10.5 multiplied by the pounds of lobster sold is $215.25.  

Expressed in an equation this is: x*5.25+y*10.5=215.25 Equation (B)

Now you have the system of equations. There are several methods to solve a system but one of the simplest is substitution.  In this method, you isolate one of the variables from one of the equations and replace it in the other equation.  

In that case, you can isolate x from equation (A): x=28.5-y

Now this variable is replaced in equation (B) and the equation is solved:

5.25*(28.5-y)+y*10.5=215.25

First apply distributive property, that is, multiply 5.25 for each term within the parenthesis:

149.625-5.25*y+10.5*y=215.25

Now the variable is located on one side of equality and the numbers that do not accompany the variable on the other side of equality. In this case it is preferable to leave the variable on the left side of the equation. Then you place 149.625 on the right side, and for that the number goes to that side with the opposite operation, which is the subtraction.  Then rearranging:

10.5*y-5.25*y=215.25-149.625

By calculating both sides of equality you get:

5.25*y=65.625

You need to clear the variable and, and for that the number 5.25 will go to the other side of equality with the opposite operation, which in this case is the division:

Finally, y=12.5

Remember that Y are the lobster pounds sold. This means that the fish market sold 12.5 pounds of lobster.

Now you replace the value of y in equation (A) to get the value of x. So x=16

This means that the fish market sold 16 pounds of  fish.