maria has $1.05 in dimes and nickels. She has 6 more nickels than dimes. How many nickels does she have?
n nickles
(n-6) dimes
5 n + 10 (n-6) = 105
11 nickles and 5 dimes
To find out how many nickels Maria has, we can set up a system of equations based on the given information.
Let's assume that the number of dimes Maria has is represented by "x". Therefore, the number of nickels she has would be represented by "x + 6", since she has 6 more nickels than dimes.
Next, we need to convert the number of dimes and nickels into cents so that we can calculate the total value.
Since a dime is worth 10 cents and a nickel is worth 5 cents, the total value of the dimes Maria has is 10x cents, and the total value of the nickels she has is 5(x + 6) cents.
According to the given information, the total value of the dimes and nickels is $1.05, which is equal to 105 cents.
So we can set up the equation:
10x + 5(x + 6) = 105
Now we can simplify and solve for "x":
10x + 5x + 30 = 105
15x + 30 = 105
15x = 105 - 30
15x = 75
x = 75 / 15
x = 5
Therefore, Maria has 5 dimes.
To find the number of nickels, we can substitute the value of x back into the expression we derived earlier: x + 6.
So, x + 6 = 5 + 6 = 11.
Therefore, Maria has 11 nickels.