Emilia saved nickels, dimes, and quarters in a jar. She had as many quarters as dimes, but twice as many nickels as dimes. If th

Answer:

Thus, Emilia has saved a total of:

                    $ 94.95

Step-by-step explanation:

We know that:

Emilia saved nickels, dimes, and quarters in a jar.

Also,

She possesses an equal number of quarters and dimes, while having twice as many nickels as dimes.

This means that:

 If the quantity of quarters in the jar is= x

The quantity of dimes in the jar is= x

and thus, the quantity of nickels in the jar is= 2x

In addition, the total number of coins in the jar is 844

which gives us the equation

x+x+2x=844

This simplifies to

4x=844

therefore

x=844/4

yielding

x=211

• Thus, the number of quarters in the jar is 211

• The number of dimes in the jar is also 211

• and hence the number of nickels in the jar = 2×211=422

• We know that:

           1 quarter= 0.25 dollar

             This means,

            211 quarters = 211×0.25=$ 52.75

• Additionally,

           1 dime= $ 0.10

             Thus,

          211 dimes = $ (0.10×211)=$ 21.10

• and

              1 nickel=$ 0.05

               Consequently,

               422 nickels = $ (422×0.05)=$ 21.10

Finally, the total value of coins in the jar is:

Total amount= $ 52.75+ $ 21.10+ $ 21.10

which totals to

Total amount= $ 94.95

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 obtain

n+d+q = 844      =>

2d +d + d = 844.

Adding up the d's, gives us

4d =844.

Dividing both sides by 4 yields

d = 211.

Hence, 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 $0.05

A 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.