Question

You have a total of 50 dimes and nickels combined. Rather than counting out how much you have yourself, you decide to use the Coinstar machine. It tells you that you had $3.10 worth of dimes and nickels. How many of each coin did you have?

a) 20 dimes and 30 nickels
b) 25 dimes and 25 nickels
c) 30 dimes and 20 nickels
d) 35 dimes and 15 nickels

Answer 1

To find the number of dimes and nickels in a collection of 50 coins that total $3.10, a system of linear equations is used. After setting the equations based on the value of dimes and nickels and solving the system, it turns out there are 12 dimes and 38 nickels.

Step-by-step explanation:

To solve the problem of determining how many dimes and nickels are in a collection of 50 coins that total $3.10, we can set up a system of linear equations. Let's use two variables: D for dimes and N for nickels. Since a dime is equivalent to $0.10 and a nickel is equivalent to $0.05, we can express the total amount of money in terms of these coins. The two equations are:

• D + N = 50 (the total number of coins)
• 0.10D + 0.05N = $3.10 (the total value of coins)

Multiplying the second equation by 100 to remove decimals gives us:

• 10D + 5N = 310

Now we can multiply the first equation by 5 to help us eliminate one of the variables:

• 5D + 5N = 250

Subtracting this from the modified second equation gives:

• 5D = 60

Dividing both sides by 5, we discover that:

• D = 12

We then substitute D = 12 back into the first equation:

• 12 + N = 50

This leads to N = 50 - 12 = 38. Therefore, the student had 12 dimes and 38 nickels.