August 2022 Algebra 1 Regents, Part IV

This exam was adminstered in August 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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August 2022

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


37. An ice cream shop sells small and large sundaes. One day, 30 small sundaes and 50 large sundaes were sold for $420. Another day, 15 small sundaes and 35 large sundaes were sold for $270. Sales tax is included in all prices.

If x is the cost of a small sundae and y is the cost of a large sundae, write a system of equations to represent this situation.

Peyton thinks that small sundaes cost $2.75 and large sundaes cost $6.75. Is Peyton correct? Justify your answer.

Using your equations, determine algebraically the cost of one small sundae and the cost of one large sundae.

Answer:

In the first part, translate the sentences in the problem into a system of equations. In the second part, substitute 2.75 and 6.75 into the system of equations and see if you get two true statements. Chances are that Peyton is wrong because the third part wants you to solve the system of equations. (This fact is NOT proof. You still need to justify your work.)

Part 1:

30x + 50y = 420
15x + 35y = 270

Part 2:

30(2.75) + 50(6.75) = 420
15(2.75) + 35(6.75) = 277.50 =/= 270

Peyton is incorrect. His values do not work for the second day.

30x + 50y = 420
15x + 35y = 270

30x + 50y = 420
-30x - 70y = -540

-20y = -120

y = 6.00

30x + 50(6) = 420
30x + 300 = 420
30x = 120
x = 4.00

A small sundae is $4.00 and a large sundae is $6.00.

End of Exam

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