Answer:
To solve this problem, we can set up a system of equations using the information given. Let x be the number of quarters, y be the number of dimes, and z be the number of nickles.
From the problem, we know that:
x:y = 8:5 (the ratio of the number of quarters to the number of dimes)
y:z = 6:11 (the ratio of the number of dimes to the number of nickles)
x+y+z = between 500 and 600 (the total number of coins)
We can start by using the first ratio to find the value of y in terms of x:
x:y = 8:5
y = (5/8)x
We can use the second ratio to find the value of z in terms of y:
y:z = 6:11
z = (11/6)y
We can substitute the value of y into the expression for z to get an expression for z in terms of x:
z = (11/6)(5/8)x
Now we can use the equation x + y + z = between 500 and 600 to find the value of x:
x + (5/8)x + (11/6)(5/8)x = between 500 and 600
Combining like terms:
(63/40)x = between 500 and 600
x = between 800 and 1000
So, x represents the number of quarters, which is between 800 and 1000.
We know that the value of a quarter is $0.25. So the total value of the quarters is between $200 and $250.
Similarly, we know that the value of a dime is $0.1 and a nickel is $0.05.
so,
y = (5/8)x
z = (11/6)(5/8)x
y = (5/8)x * $0.1 = $0.125x
z = (11/6)(5/8)x * $0.05 = $0.04166x
So, the total value of the money in the jar is $200 <= $0.25x + $0.125x + $0.04166x <= $250