Thursday, November 18, 2021

Algebra Problems of the Day (Integrated Algebra Regents, January 2012)

Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.

More Regents problems.

Integrated Algebra Regents, January 2012

Part IV: Each correct answer will receive 4 credits. Partial credit is available.

37. The sum of three consecutive odd integers is 18 less than five times the middle number. Find the three integers. [Only an algebraic solution can receive full credit.]


Consecutive integers are one after another, like n, n+1, n+2... Consecutive odd integers are each two more than the previous one, like n, n+2, n+4, where n is an odd integer.

Change the sentence in the question into an equation:

n + n + 2 + n + 4 = 5(n + 2) - 18

3n + 6 = 5n + 10 - 18

3n + 6 = 5n - 8

14 = 2n

7 = n

The numbers are 7, 9 and 11.

You could also have used n - 2, n and n + 2 and save yourself some work:

n - 2 + n + 2 = 5n - 18

3n = 5n - 18

-2n = - 18

n = 9

The numbers are still, 7, 9, and 11 becuase you used n-2, n and n+2.

End of Exam.

More to come. Comments and questions welcome.

More Regents problems.

I also write Fiction!

You can now preorder Devilish And Divine, edited by John L. French and Danielle Ackley-McPhail, which contains (among many, many others) three stories by me, Christopher J. Burke about those above us and from down below.
Preorder the softcover or ebook at Amazon.

Also, check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides.
Available in softcover or ebook at Amazon.

If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.

No comments: