Emilia saved nickels, dimes, and quarters in a jar. she had as many quarters as dimes, but twice as many nickels as dimes. if the jar had 844 coins, how much money had she saved?

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.

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