Answer:
18 1/3 payments
Step-by-step explanation:
You want to find the average number of bonuses per year over a 6-year contract that includes a base salary and a bonus for attendance.
<h3>Setup</h3>
The first step is to understand the given information and the question that is being asked. We are given a yearly salary, a per-game bonus, and a 6-year total. The question is asking how many bonuses are paid per year, on average.
The second step is to choose a way to represent the given relations so that you can answer the question that is asked. We could use a variable to represent the total number of bonuses paid over 6 years. Since we want a yearly average of the number of bonuses paid, we choose to use a variable for that value. Then we can answer the question as soon as we have found the value of the variable.
We can let 'b' represent the number of bonuses paid per year. Then the yearly earnings will be the sum of the base salary and the total of bonuses earned. Each year, the player can expect earnings of ...
base salary + bonus pay = 20,000 +8000b . . . . . yearly earnings
Then, over a period of 6 years, the player's total pay will be ...
6(20,000 +8,000b) = 1,000,000 . . . . . 6 times the pay per year
<h3>Solution</h3>
The next step is to solve the equation to find the value of the variable.
Simplifying the equation gives us ...
120,000 +48,000b = 1,000,000 . . . . . . . eliminate parentheses
48,000b = 880,000 . . . . . . . . . . . . . . subtract 120,000
b = 880000/48000 = 18 1/3 . . . . . divide by the coefficient of b
The final step is to form an answer to the question as a complete sentence, using the wording in the question.
On average the pitcher should expect 18 1/3 bonus payments each year.
