A fastpitch softball player signs a six year contract. Hear agent expects that she will earn $1000000 over the next six years. If the agent is right, how many bonus payments , on average , should the pitcher expect each year, Explain.

The correct answer is: On average , the pitcher should expect approximately 18.33 bonus payments each year

"Step-by-step solution:-
Let the number of bonus payments, expected in a year, on average be $x i.e. there will be x games with 100+ fans in a year (on average).
∴ Bonus earned in a year = number of games (with 100+fans) bonus per game
∴ Bonus earned in a year = x 8,000
∴ Bonus earned in a year = 8,000x ..................................................... (Equation i)
Yearly salary = 20,000 .......................................................................... (Equation ii)
∴ Total Earnings in a year = yearly salary + bonus
∴ Total Earnings in a year = 20,000 + 8,000x ...................................... (From Equations i & ii) .......................... (Equation iii)
Now, for 6 years, total earnings would be-
Total earnings for 6 years = 6 × Total earnings in a year
∴ Total earnings for 6 years = 6 (20,000 + 8,000x) .............................. (From Equation iii)
∴ Total earnings for 6 years = 1,20,000 + 48,000x
∴ 10,00,000 = 1,20,000 + 48,000x ................................ (From given information)
∴ 10,00,000 - 1,20,000 = 48,000x ................................................. (Taking all constants together)
∴ 8,80,000 = 48,000x
∴ 8,80,000/48,000 = x ............................................................. (Dividing both sides by 48,000)
∴ 18.33 = x
Final Answer:-
∴ On average , the pitcher should expect approximately 18.33 bonus payments each year.