Every night when Isabella came home from work she put any change she had in her pockets into a jar. One day she wanted to know how much change she had in her jar. She noticed that she had two more nickels than twice the number of dimes, and eight fewer quarters than twice the number of nickels. If the value of the quarters was $1.60 more than four times the value of the nickels and dimes together, what was the total value of the change in Isabella's jar?

my work:
n stands for nickels
d stands for dimes
q stands for quarters

n=2d+2
nickels

q=2n-8
quarters

q=$1.60+4(n+d)
total value

I can't figure out where to start getting values and what values to get.

Get an equation in terms of just one of the values.

q = 2n-8 = 2(2d-2)-8

2(2d-2)-8 = 1.60 + 4(2d-2+d)

Solve for d, then n and q.

To find the total value of the change in Isabella's jar, we need to determine the values of nickels, dimes, and quarters.

Let's start by setting up equations based on the given information:

1. The number of nickels, n, is two more than twice the number of dimes, 2d + 2.
2. The number of quarters, q, is eight fewer than twice the number of nickels, 2n - 8.
3. The value of the quarters, q, is $1.60 more than four times the value of the nickels and dimes combined, 4(n + d) + $1.60.

With these equations in mind, we can solve them simultaneously to determine the values of n, d, and q.

1. Substituting equation 1 into equation 2, we have:
q = 2(2d + 2) - 8
q = 4d + 4 - 8
q = 4d - 4

2. Substituting equation 1 into equation 3, we have:
4(n + d) + $1.60 = q
4(2d + 2 + d) + $1.60 = q
4(3d + 2) + $1.60 = q
12d + 8 + $1.60 = q
12d + $9.60 = q

Now we have two equations for q in terms of d:
q = 4d - 4
q = 12d + $9.60

Setting the two equations equal to each other, we can solve for d:

4d - 4 = 12d + $9.60
-8d = $13.60
d = -$13.60 / -8
d = $1.70

Now we can substitute this value of d back into the equations to find the values of n and q.

From equation 1:
n = 2d + 2
n = 2($1.70) + 2
n = $3.40 + 2
n = $5.40

From equation 2:
q = 4d - 4
q = 4($1.70) - 4
q = $6.80 - 4
q = $2.80

Now we know that Isabella has 5 nickels ($5.40), 1 dime ($1.70), and 7 quarters ($2.80) in her jar.

Let's calculate the total value of the change:

Total value = (value of nickels) + (value of dimes) + (value of quarters)

Total value = (5 * $0.05) + ($0.10) + (7 * $0.25)

Total value = $0.25 + $0.10 + $1.75

Total value = $2.10

Therefore, the total value of the change in Isabella's jar is $2.10.