Let's solve the problem step-by-step to find out how many dimes and nickels Jaime has.
1. Let's assume the number of nickels Jaime has is represented by "N". Therefore, the number of dimes will be "N + 14" since the number of dimes is 14 more than the number of nickels.
2. The value of each nickel is $0.05, and the value of each dime is $0.10.
3. We can now set up an equation to represent the total value of the coins. The equation is: 0.05N + 0.10(N + 14) = 2.60.
4. Simplify the equation by distributing 0.10 to N and 14: 0.05N + 0.10N + 1.40 = 2.60.
5. Combine like terms: 0.15N + 1.40 = 2.60.
6. Subtract 1.40 from both sides of the equation: 0.15N = 1.20.
7. Divide both sides of the equation by 0.15 to isolate N: N = 1.20 / 0.15.
8. Perform the division to find the value of N: N = 8.
Therefore, Jaime has 8 nickels.
To find the number of dimes, we can substitute the value of N back into our expression N + 14: 8 + 14 = 22.
Therefore, Jaime has 22 dimes.
In conclusion, Jaime has 8 nickels and 22 dimes.