August 2017 Common Core Algebra 1 Regents, Part 4

Continuing with the August 2017 Algebra 1 Regents.
Here are the Part I questions, answers, and explanations.
Here are the Part II questions, answers, and explanations.
Here are the Part III questions, answers, and explanations.

August 2017, Algebra 1 (Common Core), Part IV

A correct answer will receive 6 credits. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit.

37. Zeke and six of his friends are going to a baseball game. Their combined money totals $28.50. At the game, hot dogs cost $1.25 each, hamburgers cost $2.50 each, and sodas cost $0.50 each. Each person buys one soda. They spend all $28.50 on food and soda.
Write an equation that can determine the number of hot dogs, x, and hamburgers, y, Zeke and his friends can buy.

Graph your equation on the grid below.
Determine how many different combinations, including those combinations containing zero, of hot dogs and hamburgers Zeke and his friends can buy, spending all $28.50. Explain your answer.

Answer: There are 7 people. Each buys a soda, which are $0.50 each. .50 * 7 = $3.50.
$28.50 - 3.50 = 25.00 to spend on hot dogs and hamburgers.

The equation is 1.25x + 2.50y + 3.50 = 28.50 or 1.25x + 2.50y = 25.00
The price of a hot dog times the number of hot dogs plus the price of a hamburger times the number of hamburgers plus the price of the sodas equals $28.50. Note that the question states that all the money was spent and that you are looking for an equation, not an inequality.

The number of $1.25 hot dogs that can be bought for $25.00 is 20. The number of $2.50 hamburgers that can be bought is 10.
There will be 11 possible combinations, which appear on the graph below. You don't need to list them, but they are:
(20, 0), (18, 1), (16, 2), (14, 3), (12, 4), (10, 5), (8, 6), (6, 7), (4, 8), (2, 9), (0, 10).

Here is the graph:

End of Part IV
End of Exam

How did you do?

Reminder: I've been asked not to post the questions to newer exams for at least a week after it.
So I probably won't be able to write up the answers to today's tests until after February 1.
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