Representing with equations

A high school is having a talent contest and will give different prizes for the best five acts in the show.  First place wins the most money and each place after that wins $50 less than the previous place.  

​Use the information provided to answer Part A and Part B.

Part A
Create a model that can be used to determine the total amount of prize money based on the amount of the first prize.

Part B
The talent contest has a total of $1,000 in prize money.  What is the amount of money for each of the five prizes?  Show your work.

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Part A
x = amount of money for first place
P = total amount of money

P = x + (x – 50) + (x – 100) + (x – 150) + (x – 200)  {model showing first place wins most, 
                                                                                          each place after is $50 less than previous}                                                                                                       

Part B
x + (x – 50) + (x – 100) + (x – 150) + (x – 200) = 1000   {set the total equal to $1000}
x + x – 50 + x – 100 + x – 150 + x – 200 = 1000   {removed parentheses}
5x – 500 = 1000   {combined like terms}
       +500   +500
5x = 1500   {added 500 to each side}
x = 300   {divided each side by 5}

1st place = $300
2nd place = $250
3rd place = $200
4th place = $150
5th place = $100

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