Elena has 15 more dimes than nickels. If she has $2.55, how many nickels does she have?
add up the value of all the coins:
5n + 10(n+15) = 255
To solve this problem, we can set up a system of equations. Let's denote the number of nickels as 'n' and the number of dimes as 'd'.
According to the problem, Elena has 15 more dimes than nickels, so we can write:
d = n + 15 (Equation 1)
We also know that the total value of the dimes and nickels is $2.55. Since a nickel is worth $0.05 and a dime is worth $0.10, we can write the second equation as:
0.05n + 0.10d = 2.55 (Equation 2)
To solve this system of equations, we can substitute Equation 1 into Equation 2.
0.05n + 0.10(n + 15) = 2.55
0.05n + 0.10n + 1.50 = 2.55
0.15n + 1.50 = 2.55
0.15n = 2.55 - 1.50
0.15n = 1.05
Divide both sides of the equation by 0.15:
n = 1.05 / 0.15
n = 7
Therefore, Elena has 7 nickels.