June 2022 Algebra 1 Regents, Part IV

This exam was adminstered in June 2022. These answers were not posted until they were unlocked on the NY Regents website or were posted elsewhere on the web.

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June 2022

Part IV: A correct answer will receive 6 credits. Partial credit can be earned.


37. At an amusement park, the cost for an adult admission is a, and for a child the cost is c. For a group of six that included two children, the cost was $325.94. For a group of five that included three children, the cost was $256.95. All ticket prices include tax.

Write a system of equations, in terms of a and c, that models this situation.

Use your system of equations to determine the exact cost of each type of ticket algebraically.

Determine the cost for a group of four that includes three children.

Answer:

If you don't get the two equations correct, the rest will be difficult. Important: Keep going. You can get partial credit for consistent work but only if you finish the problem and get an answer. Yes, the person scoring the exam will go through your work.

This is the first time that I remember a question saying "a group of six including two children" meaning that there are only 4 adults.

The equation for the first group is 4a + 2c = 325.94

The equation for the second group is 2a + 3c = 256.95

You can solve this system using elimination because 2a is a factor of 4a.

4a + 2c = 325.94
2a + 3c = 256.95

4a + 2c = 325.94
-4a - 6c = -513.90
-4c = -187.96

c = 46.99

4a + 2(46.99) = 325.94

4a + 93.98 = 325.94

4a = 231.96

a = 57.99

An adult ticket costs $57.99 and a child's ticket costs $46.99.

You can answer the last question through substitution into the expression a + 3c, or you use the amount provided in the quation for 2a + 3c and subtract c.

Method 1: 57.99 + 3(46.99) = 198.96

Method 2: 256.95 - 57.99 = 198.96

End of Exam

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