Ace the Officer Aptitude Rating (OAR) 2025 – Unleash Your Inner Officer!

Question: 1 / 400

A cash box contains 63 dimes, 33 nickels, and the rest are quarters. If the probability of selecting a quarter is 1/5, how many quarters does the box contain?

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To determine the number of quarters in the cash box, we start by understanding the total quantity of coins and the given probability of selecting a quarter.

Firstly, we know the number of dimes and nickels:

- Dimes: 63

- Nickels: 33

To find the total number of dimes and nickels, we add these two figures together:

63 (dimes) + 33 (nickels) = 96 coins.

Let \( x \) represent the number of quarters. The total number of coins in the cash box is then:

96 (dimes and nickels) + \( x \) (quarters) = 96 + \( x \).

According to the problem, the probability of selecting a quarter is given as \( \frac{1}{5} \). The probability is calculated by dividing the number of quarters by the total number of coins. This gives us the equation:

\[

\frac{x}{96 + x} = \frac{1}{5}.

\]

To solve for \( x \), we can cross-multiply:

\[

5x = 1(96 + x).

\]

Simplifying this leads to:

\[

5x = 96 + x.

\

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