a farmer makes a profit of x cents on each of the (x+5) eggs her hen lays. if her total profit was 84 cents find the number of eggs the hen lays

Given: A farmer makes a profit of x cents on each of the (x + 5) eggs her  hen lays.

To find: The number of eggs  the hen lays.

Solution:

Now we have given that farmer makes a profit of x cents on each of the (x + 5) eggs her  hen lays.

That means the farmer has x + 5 eggs, which also means that each egg can make a profit of x percent.

Then the equation formed will be:

               x × ( x + 5 ) = 84

                x^2 + 5x - 84 = 0

               (x - 7) (x + 12) = 0

               x = 7 , -12

The positive solution will be considered, so the answer is 7+5 = 12 eggs

               The number of eggs  the hen lays is 12.