a company made a profit of $8.6 million in its first year. it lost $5.9 million in its second year and lost…

Explanation:

Step1: Recall average formula

The formula for the average of a set of numbers is $\text{Average}=\frac{\text{Sum of values}}{\text{Number of values}}$. Let the profit or loss in the first year be $P_1 = 8.6$ million, in the second year be $P_2=- 5.9$ million (negative for loss), in the third year be $P_3 = - 6.3$ million, and in the fourth year be $P_4$.

Step2: Calculate sum for average in first - three years

We know that the average profit or loss over the first three years is what we want to find first. The sum of the values for the first three - year period, $S_1=P_1 + P_2+P_3$. So $S_1=8.6+( - 5.9)+( - 6.3)=8.6 - 5.9 - 6.3=8.6-(5.9 + 6.3)=8.6 - 12.2=-3.6$ million. The number of values $n_1 = 3$. Then the average $A_1=\frac{S_1}{n_1}=\frac{-3.6}{3}=-1.2$ million.

Step3: Use break - even condition for four years

Since the company broke even over the first four years, the total sum of profits and losses over four years is $0$. That is $P_1 + P_2+P_3+P_4 = 0$. We know $P_1 + P_2+P_3=-3.6$ million. Substituting into the equation $-3.6+P_4 = 0$. Solving for $P_4$, we get $P_4 = 3.6$ million.

Answer:

a) The average profit or loss per year over the first three years is -$1.2$ million. b) The profit or loss in the fourth year was $3.6$ million.