Steven had $2.50 in nickels and quarters

Steven had $2.50 in nickels and quarters. He had one less than two times as many quarters as he had Nichols. How many of each coin did he have?

The correct answer and explanation is:

Correct Answer:
Steven had 5 nickels and 9 quarters.

Explanation (300 words):
To find out how many nickels and quarters Steven had, start by defining variables. Let the number of nickels be n and the number of quarters be q.

According to the problem:

• The total value of all coins is \$2.50. This is equal to 250 cents.
• A nickel is worth 5 cents, and a quarter is worth 25 cents.
• Also, the number of quarters is one less than twice the number of nickels. That is written as:
  q = 2n – 1

Now use the value information to write an equation involving the total amount:

• Total value from nickels = 5n
• Total value from quarters = 25q
  So:
  5n + 25q = 250

Now substitute the expression for q (from q = 2n – 1) into the value equation:
5n + 25(2n – 1) = 250

Distribute the 25:
5n + 50n – 25 = 250

Combine like terms:
55n – 25 = 250

Now solve for n:
55n = 275
n = 5

Now plug n = 5 back into the expression for q:
q = 2n – 1 = 2(5) – 1 = 9

So, Steven had 5 nickels and 9 quarters.

To confirm:

• 5 nickels = 5 × 5 = 25 cents
• 9 quarters = 9 × 25 = 225 cents
• Total = 25 + 225 = 250 cents = \$2.50

This satisfies both conditions: the total value is \$2.50, and the number of quarters is one less than twice the number of nickels. Therefore, the solution is correct.