Question

When Stretch Gordon signed a contract to play basketball for the Toronto Raptors, he received a one-time $250 000 signing bonus. His contract said that he would also receive $100 000 for each game he plays.

The Raptors are scheduled to play 85 games this season.

Create a table of values that will show some of the possible amounts Stretch might earn throughout the first season. Number of games played is represented by n and money earned by E.
Graph the information to show his earnings for the season. Use a suitable scale. Change the money values in your table to millions of dollars before starting.
i) Write an equation relating Stretch's earnings to the number of games he plays.
ii) Define your variables, including units.
iii) Explain what the numbers in your equation represent for Stretch.
How much money will Stretch make if he plays 44 games this season? Show your work.
Stretch's twin brother, Rory, has been offered a different contract. The following equation defines the offer: E = 95 000n + 450 000
E represents Rory's total earnings in dollars and n represents the number of games Rory plays. Is this a better offer than Stretch's? Give reasons for your answer by comparing the two offers, reporting mathematical details about the comparison.

Answer 1

Here's what I get

Explanation:

Stretch

(i) The equation

E = 250 000 + 100 000n

(ii) Variables

n = the number of games played

E = Stretch's total earnings in dollars

(iii) Constants

$250 000 = Stretch's signing bonus

$100 000 = the money earned for each game.

`\begin{array}{ccc}\textbf{Games played} & \textbf{ Earnings/}\mathbf{\$}&\textbf{Earnings/}\mathbf{\$10^(6)} \\20 & 2 350 000 &2.35\\40 & 4 250 000&4.25 \\60 & 6 150 000 &6.15\\80 & 8 050 000&8.05 \\\end{array}`

The graph shows how Stretch's total earnings vary with the number of games played.

(iv) Total earnings after 44 games

`\begin{array}{rcl}E & = & 250000 + 100000n\\& = &250000 + 100000(44)\\& = &250000 + 4400000\\& = & \mathbf{4 650 000}\\\end{array}`

Rory

E = 95 000n + 450 000

Rory's deal is better than Stretch's if they play fewer than 40 games.

He starts off with a bigger signing bonus, but Stretch earns more money per game.

Stretch closes the gap with each game played.

By 40 games they have the same total earnings.

After 40 games Stretch has more total earnings.