Part ACreate a model that can be used to determine the total amount of prize money based on the amount of the first prize. |
Part BThe 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. |

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

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.

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.

__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

2nd place = $250

3rd place = $200

4th place = $150

5th place = $100

*Ask Algebra House*