Let us assume number of nickels = n,
number of dimes = d and
number of quarters = q.
Total number of coins = 844.
We can setup a statement "number of nickels + number of dimes +number of quarters = Total coins.
And we can setup an equation for the above statement as
n+d+q = 844 ---------------------equation(1).
We also given: Emilia had as many quarters as dimes.
Therefore, number of quarters = number of dimes.
So, we can setup another equation as
q = d ------------------------equation(2).
Also given : "twice as many nickels as dimes".
We can setup another equation for this statement as
n = twice of number of dimes
or n= 2d -------------------------- equation (3).
We got three equations.
Let us solve system of three equation by substitution method.
Substituting q = d and n= 2d in equation (1), we got
n+d+q = 844 => 2d +d + d = 844.
Adding d's, we get
4d =844.
Dividing both sides by 4, we get
d = 211.
Therefore number of dimes = 211.
Let us find number of nickels and number of quarter coins now.
We know, number of quarters = number of dimes.
Therefore, number of qurters = 221.
Total number of coins = 844.
Therefore, number of nickels = 844 - (number of quarters + number of dimes).
= 844 -(221+221) = 844 - 442
= 402.
So, the number of nickels =402.
Let us find the total values of all the coins.
A nickel = $0.05
A dime = $0.10
A quarter = $0.25.
Total value = 0.05 *(number of nickels) + 0.10*(number of dimes) + 0.25*(number of quarters).
= 0.05* 402 + 0.10 *221 + 0.25*221.
= 20.10 + 22.10 + 55.25.
= 97.45.
Therefore, total value of all 844 coins = $97.45.
Emilia had saved $97.45.
