Let's denote:
- D = number of dimes
- Q = number of quarters
- N = number of nickels
We have three equations based on the given information:
1. D = 2Q (Sama has twice as many dimes as quarters)
2. N = Q + 17 (Sama has 17 more nickels than quarters)
3. D + Q + N = 65 (Sama has a total of 65 coins)
We can use these equations to solve for the values of D, Q, and N.
From equation 1, we can substitute D = 2Q into equation 3:
2Q + Q + (Q + 17) = 65
4Q + 17 = 65
4Q = 48
Q = 12
Now that we have the value of Q, we can find the values of D and N using equations 1 and 2:
D = 2 * 12 = 24
N = 12 + 17 = 29
So, Sama has 24 dimes, 12 quarters, and 29 nickels.
To find the total value, we calculate:
Total value = (value of dimes) + (value of quarters) + (value of nickels)
Value of dimes = 24 * $0.10 = $2.40
Value of quarters = 12 * $0.25 = $3.00
Value of nickels = 29 * $0.05 = $1.45
Total value = $2.40 + $3.00 + $1.45 = $6.85
Therefore, Sama's coins are worth $6.85.
