Kim has $4.75 in nickels and dimes. If she has twice as many dimes as nickels, how many of each coin does she have?
0.05n + 0.1d = 4.75
d = 2n
0.05n + 0.1(2n) = 4.75
0.25n *100 = 4.75 8100
25n = 475
25n/25 = 475/25
n = 19
d = 2n
d = 2(19)
d = 38
dimes = 38
nickels =19
To solve this problem, we can use algebraic equations.
Let's say the number of nickels that Kim has is represented by the variable 'n', and the number of dimes is represented by the variable 'd'.
Given that Kim has $4.75 in total, we can express this mathematically as:
0.05n + 0.10d = 4.75
We also know that she has twice as many dimes as nickels, so we can write the equation:
d = 2n
Now we have a system of two equations with two variables. We can solve this system using substitution or elimination.
Substituting the value of 'd' from the second equation into the first equation, we have:
0.05n + 0.10(2n) = 4.75
Simplifying this equation, we get:
0.05n + 0.20n = 4.75
0.25n = 4.75
Dividing both sides of the equation by 0.25, we find:
n = 4.75 / 0.25
n = 19
So Kim has 19 nickels.
Substituting this value back into the second equation, we can determine the number of dimes:
d = 2(19)
d = 38
Therefore, Kim has 19 nickels and 38 dimes.