Let’s define the number of nickels as n,
the number of dimes as d, and
the number of quarters as q.
The total quantity of coins is 844.
We can express this as "number of nickels + number of dimes + number of quarters = Total coins.
Thus, we can form an equation from this statement as
n+d+q = 844 ---------------------equation(1).
Additionally, it is given that Emilia possesses as many quarters as dimes.
Consequently, the number of quarters equals the number of dimes.
This leads to another equation:
q = d ------------------------equation(2).
It is also stated that there are "twice as many nickels as dimes."
We can create a further equation representing this statement as
n = two times the number of dimes
or n= 2d -------------------------- equation (3).
Three equations have been established.
Let’s solve this system of three equations using substitution methods.
By substituting q = d and n= 2d into equation (1), we obtainn+d+q = 844 =>2d +d + d = 844.
Adding up the d's, gives us 4d =844.Dividing both sides by 4 yieldsHence, the quantity of dimes = 211.
Next, we will determine the number of nickels and quarters.We know that the number of quarters equals the number of dimes.
Thus, the total count of quarters is 211.The overall quantity of coins sums to 844.Hence, the number of nickels = 844 - (sum of quarters and dimes).= 844 -(211+211) = 844 - 422
= 422.
Therefore,the total of nickels = 422.
Now, let’s compute the total values of all coins.A nickel is valued at $0.05A dime is valued at $0.10
A quarter is valued at $0.25.The total value = 0.05 *(number of nickels) + 0.10*(number of dimes) + 0.25*(number of quarters).
=[ 0.05* 422 + 0.10 *211 + 0.25*211].= 21.10 + 21.10 + 52.75.= 94.95.
So, the total worth of all 844 coins = $94.95.Emilia saved $94.95.