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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