Question

There are two more quarters than dimes, and as many nickels as quarters and dimes together. The total amount of money is $3.75. How many quarters, dimes, and nickels are there?

a. 1 quarter, 3 dimes, 2 nickels
b. 2 quarters, 4 dimes, 3 nickels
c. 3 quarters, 5 dimes, 4 nickels
d. 4 quarters, 6 dimes, 5 nickels

Answer 1

To solve the problem, set up an equation using the given information. Simplify the equation to find the value of x, which represents the number of dimes. Use the value of x to find the number of quarters and nickels. The solution is 9 dimes, 11 quarters, and 20 nickels.

Step-by-step explanation:

To solve this problem, let's break it down step by step. Let's assume the number of dimes is x:

1. There are two more quarters than dimes. So the number of quarters is x + 2.
2. The number of nickels is the same as the total of quarters and dimes. So the number of nickels is (x + 2) + x = 2x + 2.
3. The value of the quarters is 25 cents each, so the total value of the quarters is (x + 2) * 25.
4. The value of the dimes is 10 cents each, so the total value of the dimes is x * 10.
5. The value of the nickels is 5 cents each, so the total value of the nickels is (2x + 2) * 5.
6. The total value of the coins is $3.75 which is equal to 375 cents. So we can set up the equation: (x + 2) * 25 + x * 10 + (2x + 2) * 5 = 375.
7. Simplifying this equation, we get 35x + 60 = 375.
8. Subtracting 60 from both sides of the equation gives us 35x = 315.
9. Dividing both sides of the equation by 35 gives us x = 9.

So, there are 9 dimes, 9 + 2 = 11 quarters, and 2(9) + 2 = 20 nickels.