Final answer:
To find out how many nickels Jim has among his 44 nickels and dimes that total $2.95, we solve a system of equations. After setting the equations up and solving them, we find that Jim has 29 nickels.
Step-by-step explanation:
Jim has a total of 44 nickels and dimes worth $2.95. To determine how many nickels he has, we can set up a system of equations using the given information. We denote the number of nickels as n and the number of dimes as d. The value of a nickel is 5 cents, and the value of a dime is 10 cents.
From the problem, we have two equations:
- n + d = 44 (total number of coins)
- 5n + 10d = 295 (total value in cents)
To solve the system, we can multiply the first equation by 5, which gives us:
5n + 5d = 220 5n + 10d = 295
Subtracting the first equation from the second, we get:
5d = 75
Dividing by 5, we find that:
d = 15
Substituting the value of d back into equation 1:
n + 15 = 44
n = 44 - 15
n = 29
Therefore, Jim has 29 nickels.