Again, I have 23195 trophies. A season reset occurs 4 times per year or about every 90 days. A season reset deducts 33% of your trophies over 10000. Trophies 10000 and under cannot be taxed or accounted for. Additionally, the amount of trophies taxed is always a whole number, and is always rounded up. For example, if I had 10001 trophies, I would be taxed 1 trophy after 1 season reset. After how many season resets, will be 23195 trophies become 10000? What expression can I use to solve?
First, we need to calculate how many trophies will be deducted after each season reset.
33% of (23195 - 10000) = 43.98 ≈ 44 trophies
Since the number of trophies taxed is always rounded up, we will assume that 44 trophies will be deducted after each season reset.
Let x be the number of season resets it takes to reach 10000 trophies.
Starting with 23195 trophies, the number of trophies remaining after x season resets can be expressed as:
23195 - (x * 44)
We want to find the value of x when the number of trophies remaining is equal to 10000:
23195 - (x * 44) = 10000
Simplifying,
x = (23195 - 10000) / 44
x = 348.07 ≈ 349
Therefore, it will take approximately 349 season resets for 23195 trophies to become 10000.
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To determine the number of season resets it will take for your 23195 trophies to become 10000, we need to subtract 33% of the trophies over 10000 at each reset until it reaches or drops below 10000.
Let's break down the steps to solve this problem.
1. Determine the number of trophies that are subject to taxation. Since trophies 10000 and below are not taxed, we subtract 10000 from the initial number of trophies: 23195 - 10000 = 13195.
2. Apply the 33% deduction to the trophies subject to taxation. Multiply 13195 by 0.33 to calculate the number of trophies deducted: 13195 * 0.33 = 4353.35. Since the number of trophies deducted should be a whole number rounded up, we round up 4353.35 to 4354.
3. Subtract the rounded-up deduction from the total trophies. Subtract 4354 from 13195: 13195 - 4354 = 8841.
4. Repeat steps 2 and 3 until the trophy count drops to or below 10000.
Using an expression, we can represent the number of trophies after each reset as follows:
Trophies after reset = Initial trophies - (0.33 * (Initial trophies - 10000)).
To determine after how many season resets your trophies will become 10000, we need to solve the equation:
10000 = 23195 - (0.33 * (23195 - 10000))
Simplifying the equation:
10000 = 23195 - (0.33 * 13195)
Now we can solve for the unknown value.