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This post is a solution to a problem you might be struggling with in algebra 2. It talks about mindful manipulation of percents and sales tax, and it's really not that hard. As long as you understand the basics, this one will be easy. For example, if you're given $4 for items costing $2, what would the total cost be? Well, if we do the math that would be 100%, since it is 4/2 = 2x or 2+2 = 4. We can apply that to other situations, though. But let's try something else. If you have $4 for items that cost $2, there are four possibilities: 1.) Nothing costs $2! Everything costs more than $2, so the total value is 4x-4=8-4=12. 2.) One thing costs exactly 2. It's worth 2x, so the total value is 4x-4=16-4=12. 3.) Two things cost exactly 2! The total value is 2(x+6)=2(8)=16. 4.) The total value is $2x+6, which equals $12. All you have to do is divide all the different cases by two, and then subtract the smallest possible value from that number. In the first example, just subtract 4 from 12. To apply this example to sales tax, let's say you have a sale for items costing $2 each. There are four possibilities: 1.) Nothing costs $2! Everything costs more than $2 so there's a total value of 4x-4=8-4=12. This means there is no sales tax at all because it's exactly 0%. 2. There are two items that cost $2 each, so the total value is 2(x+6)=2(8)=16. This means there is 6% in sales tax. 3.) There are four items that cost $2 each, so the total value is 2(4+6)=2(10)=20. This means there is 10% in sales tax. 4.) The total value equals $2x+6=12, which means there is no sales tax at all because it's exactly 0%. This simple formula works for many other situations involving money and percents, like this one: Let's say you make an alphabetical list of all of your expenses that costs $50 dollars altogether. It goes like this: A,D,B,C,E,F. You want to make a new list with the alphabetical order switched around. How much do you need to add to each letter? Well, if you're smart you can find out without too much trouble. Just say that the total cost is $50. This means that A-E has an average cost of 5/6 or 5/6*50 = 30. Now let's see what each letter has to be increased by: A - $30 (original value -$10). D - $30 (original value -$10). B - $40 (original value +$10). cfa1e77820
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