Sarah has $4.55 worth of change in nickels and dimes. If she has 5 times as many nickels as dimes, how many of each type of coin does she have?
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.
We're given two pieces of information:
1. The total value of the coins is $4.55. Since one nickel is worth $0.05 and one dime is worth $0.10, we can express this information as an equation:
0.05N + 0.10D = 4.55
2. Sarah has 5 times as many nickels as dimes. This can also be expressed as an equation:
N = 5D
Now we have a system of two equations. We can solve this system using substitution or elimination.
Using substitution, we substitute N in the first equation with its equivalent value from the second equation (N = 5D):
0.05(5D) + 0.10D = 4.55
0.25D + 0.10D = 4.55
0.35D = 4.55
To solve for D, divide both sides of the equation by 0.35:
D = 4.55 / 0.35
D ≈ 13
Now, substitute the value of D back into the second equation to find N:
N = 5D
N = 5(13)
N = 65
Therefore, Sarah has 65 nickels and 13 dimes.
number of dimes --- d
number of nickels --- 5d
10d + 5(5d) = 455
35d=455
d=13
state your conclusion.