Abby plans to purchase pencils as prizes for the school fair. The pencils cost $11.52 per case or can be purchased individually. With her available money,

Abby can either buy ten cases of pencils and eight individual pencils or she can buy 1160 individual pencils. In either situation she will not have any money remaining after the purchases. How much money does Abby have?

11.52(10) + 8x = 1160x

where x is the cost of a pencil.

115.20 =1152x

x = .1 or 10 cents.

1160 time .1 is $116

11.52(10) + .1(8)
115.2 = .8 = $116

Well, it seems like Abby has quite a pencil obsession! It's good to know she's all "write" in the school fair spirit. Now, let's do some math to figure out how much money she has.

First, let's consider the scenario where she buys ten cases of pencils and eight individual pencils. Each case costs $11.52, so the total cost of ten cases would be 10 * $11.52 = $115.20. Additionally, purchasing eight individual pencils would cost 8 * $11.52 = $92.16.

In the other scenario, Abby wants to buy 1160 individual pencils. Since we know the individual pencils cost the same as the case of pencils, we can multiply the number of individual pencils by the price of one case: 1160 * $11.52 = $13,363.20.

Now, since in both scenarios Abby doesn't have any money remaining, we can assume that her available money is equal to the total cost of all the pencils. Therefore, Abby must have $115.20 + $92.16 = $207.36 in her piggy bank.

So, Abby has $207.36 to spend on pencils. Remember, laughter is free, though!

Let's assume that Abby has $x.

If Abby buys ten cases of pencils and eight individual pencils, the total cost would be 10 * $11.52 + 8 * price of an individual pencil.
Since she doesn't have any money remaining after the purchase, we can say that:

10 * $11.52 + 8 * price of an individual pencil = $x

Similarly, if Abby buys 1160 individual pencils, the total cost would be 1160 * price of an individual pencil. And again, since she doesn't have any money remaining after the purchase, we can say that:

1160 * price of an individual pencil = $x

Now we have two equations:

10 * $11.52 + 8 * price of an individual pencil = $x

1160 * price of an individual pencil = $x

We can solve these equations to find the value of $x.

To solve this problem, we can set up two equations based on the given information and solve for the "available money" that Abby has.

Let's assume the available money Abby has is 'x' dollars.

1) If Abby buys ten cases of pencils and eight individual pencils:
The cost of one case of pencils is $11.52, so the cost of ten cases will be 10 * $11.52 = $115.20.
The cost of eight individual pencils is not given, so let's assume it's 'y' dollars.
So, the total cost of ten cases and eight individual pencils will be $115.20 + y dollars.
According to the problem, she will not have any money remaining after the purchase, so the equation becomes:
115.20 + y = x

2) If Abby buys 1160 individual pencils:
The cost of one individual pencil is not given, so let's assume it's 'z' dollars.
So, the total cost of 1160 individual pencils will be 1160 * z dollars.
According to the problem, she will not have any money remaining after the purchase, so the equation becomes:
1160z = x

Now, we have two equations:
115.20 + y = x ----(1)
1160z = x ----(2)

To find the value of 'x' (the available money Abby has), we need to find the values of 'y' and 'z' first.

According to the problem, the available money is the same in both situations, so we can equate equations (1) and (2):
115.20 + y = 1160z

Now, let's consider different values for 'y' and 'z' to find the possible values of 'x'.

If we assume 'y' as 0 and 'z' as 0.10, then the equation becomes:
115.20 + 0 = 1160 * 0.10
115.20 = 116

This is not a valid solution.

Let's try another set of values:
Assume 'y' as 0.08 and 'z' as 0.10, then the equation becomes:
115.20 + 0.08 = 1160 * 0.10
115.28 = 116

This is also not a valid solution.

Based on these calculations, it seems there is no valid value for 'x' that satisfies both equations. Therefore, it appears there is either missing information or an error in the problem statement.

In conclusion, we cannot determine how much money Abby has based on the given information.