January 2024 Algebra 1 Regents Part IV

This exam was adminstered in January 2024.

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January 2024

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


37. Jim had a bag of coins. The number of nickels, n, and the number of quarters, q, totaled 28 coins. The combined value of the coins was $4.

Write a system of equations that models this situation.

Use your system of equations to algebraically determine both the number of quarters, q, and the number of nickels, n, that Jim had in the bag.

Jim was given an additional $3.00 that was made up of equal numbers of nickels and quarters. How many of each coin was he given? Justify your answer.

Answer:

Write one equation for the total number of the nickels and quarters, and then write a second equation for the total value of those nickels and quarters. n + q = 28
5n + 25q = 400

Use substition or elimination to solve the equation. For example, you could replace q with 28 - n.

5n + 25(28 - n) = 400

5n - 25n + 700 = 400

-20n = -300

n = 15

15 + q = 28

q = 13

If he was given an equal amount of nickels and quarters, then n = q. Therefore,

5q + 25q = 300
30q = 300
q = 10
n = 10

He received 10 more nickels and 10 more quarters.

End of Exam

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