Question

The math club sold candy bars and made $9.50 in coins alone. They collected an equal number of dimes and nickels and 10 fewer quarters than nickels. How many of each did they collect.

Answer 1

The math club collected 30 dimes, 30 nickels, and 20 quarters.

Step-by-step explanation:

Let's solve this problem step by step:

1. Let's assign variables to represent the quantities of dimes, nickels, and quarters. Let's say the number of dimes is 'x', the number of nickels is 'x', and the number of quarters is 'x - 10'.
2. The value of the dimes can be represented as 10 cents multiplied by the number of dimes, which is 10x cents.
3. The value of the nickels can be represented as 5 cents multiplied by the number of nickels, which is 5x cents.
4. The value of the quarters can be represented as 25 cents multiplied by the number of quarters, which is 25(x - 10) cents.
5. According to the problem, the total value of the coins is $9.50. So we can set up the equation: 10x + 5x + 25(x - 10) = 950 cents.
6. Simplifying the equation, we get 10x + 5x + 25x - 250 = 950.
7. Combining like terms, we get 40x - 250 = 950.
8. Add 250 to both sides of the equation to isolate the variable, giving us 40x = 1200.
9. Divide both sides of the equation by 40 to solve for 'x', which gives us x = 30.

Therefore, the math club collected 30 dimes, 30 nickels, and 20 quarters.