Question

Bob has 37 coins totaling $2.45. If he only has dimes and nickels, how many of each coin does he have?

a) 12 dimes and 25 nickels
b) 23 dimes and 14 nickels
c) 15 dimes and 22 nickels
d) 18 dimes and 19 nickels

Answer 1

To solve the coin problem, we can use a system of equations and determine that Bob has 12 dimes and 25 nickels.

Step-by-step explanation:

The student is asking for help with a mathematical problem involving a system of equations. The question involves determining the number of dimes and nickels that Bob has, given the total amount of money and the total number of coins.

Let's define two variables: let d represent the number of dimes and n represent the number of nickels. We can establish two equations based on the information given:

1. d + n = 37 (since there are 37 coins in total)
2. 0.10d + 0.05n = $2.45 (since the value of the dimes and nickels adds up to $2.45)

To solve this system of equations, we can multiply the second equation by 100 to get rid of the decimals:

1. 10d + 5n = 245

Now, we can multiply the first equation by 5 and subtract it from the modified second equation to solve for d:

1. 5d + 5n = 185
2. (10d + 5n) - (5d + 5n) = 245 - 185
3. 5d = 60
4. d = 12

Substituting d = 12 back into the first equation gives us n:

1. 12 + n = 37
2. n = 25

So Bob has 12 dimes and 25 nickels.