[morgaine300]

Romesfall, your instincts about some of this being incorrect is right. 1 & 3 are both being done incorrectly. Both of them are percentage reductions, where you are given the number after the reduction. I don't know if you're supposed to be using algebra to solve these, but there's an easier way. If you like an algebraic way, that is fine, but the setup is still incorrect.

The reason is that if the number you're given is after the reduction has already happened, the percent given is a percent of an unknown number, so you're actually trying to work back to a number. Wondergirl had the right concept on #3, but didn't play it out right. And #1 just isn't right. Both of them can be solved in the same manner because they are the same problem.

If something was sold at $30 and that's a loss of 6%, that means it's a loss off the original cost, not 6% of the $30. You said in one post that it seems the original should be a bigger number. Yes. But not 31.80 or whatever that was. It's not 6% of $30. It's:

Cost to seller - 6% loss on that cost = sales price

You see that it's 6% of that unknown cost, not the sales price. So taking 6% of $30 doesn't work.

Same with #3. The 318.75 is the price the customers paid, after a reductino of 15%. The 15% was on the originally marked price:

Original price - 15% of original price = sales price.

Check your answers. Is 1.80 6% of 31.80? No. So $1.80 isn't the loss off the original price. What is 15% of $340? Because it was marked down 15 off the original. As you'll see, that isn't going to get you to a price of $318.75. Check your answers and see if they work out. (Although this could be interpretation too.)

Notice they both are the same thing? So they can be solved the same way.

Here's a fairly easy way you can solve for these increase/decrease problems like this. What they are giving you is a number after the decrease already happened, which means the percent they're giving is on some unknown original number. So you have to work backwards. Working a multiplication backwards means dividing something.

If I have an original number and I take 5% off, how much in percent do I have left? 95%. So if I put something on sale at 5% off and sell it for $60, that $60 sales price is 95% of the original. All I'm doing is subtracting the discounted percent off 100%. That's for a decreased number. Once I have that percent, I divide the already-decreased number by .95. $60/.95 = $63.16. So 63.16 was my original price. I can check that. 63.16 x 5% = $3.16 discounted amount. 63.16 - 3.16 = $60 reduced amount.

Doing that by algebra would be:
x - .05x = 60
There's an understood 1 on the x. So 1x - .05x = .95x. Combining like terms.
So
.95x = 60.
Divide .95 out of both sides...
... same thing I just did the non-algebra way.

Try this method on #1 and #3 and see what you get.

[morgaine300]

I'm going to try a pictorial using lines. It's kind of squished up and not as easy to read as I would like, but I had to fit into a certain space. Hopefully it's easier to read than I think. :D This works better when I can do it in person.

Remember that all percents are based on 100%. So 100% is like the "original" of something, or the whole amount, depending on what it's being applied to. When you're doing increases and decreases, it's the original. Then you decrease by a percent or increase by a percent, and of course get to some other number. If you have the original, you multiply. But these are problems where you have the number after a change has occurred, so you are solving for the original number.

So you're either subtracting from, or adding to, an original number that was 100%. So you have to find the percent of the new number and go backwards. It will be a division. Since percents can be divided up into two or more pieces, always make sure you use the correct corresponding number. For example, in the decrease problem, you don't have the 5% so you don't use that percent. The $60 is the 95% left over. So match that up.

The other one is an increase problem. I don't know if you've got any of those. You can ignore it if you like. Well, you can ignore the whole post if you like :), but this will always work. For an increase, you're going above 100% to something bigger. Again, in that second example, you don't have the 10%. You have a number that corresponds to 110% so that's the one you have to use.

If you knew the discount on the sale item was 3.16 but didn't know the $60, you could divide by 5% (.05) to get back to the original. That works too.

[morgaine300]

And if you can put up with me, one more thing.

#2 came out correctly. However, learn the math behind it and not just how to do problem #2. (Of course, you need to practice problems to get the hang of it.) I tutor college students in accounting and some math, and they still can't do this, even though it comes up in accounting over and over and over again. But they all work the same way.

Any time you want to know what percent one number is of another number, you divide in that order. I have 10 pieces of fruit. 6 of them are apples. What percent are the apples of the total fruit? Divide in that order: apples/fruit = 6/10 = .6 (60%) It's basically a proportion of them. You see that?

You made $1200 this month. You put $110 of that into your savings account. What percent did you save? That is, what percent is the $110 you saved OF the $1200 you made? Divide in order: 110/1200 = .09 (rounded) or 9%.

It works for anything. You can apply it to money, people, inventory items, the amount of calcium in milk, whatever.

What percent is glijsf's of weilfs'? Divide glijsf/weilf. It still works. See, I don't even need to know what it is.

One trick is that there isn't any percent given in these. You are solving for the percent. You're wanting to know what percent one thing is OF another thing. That's when it works. You're not solving an increase/decrease sort of thing. Just simply what percent is a OF b. a/b

Of course, sometimes you have to do something else first. Shop pays $11 for CDs and sells them for $16. It wants to know the percent of the profit. Well, you can't divide those 2 numbers in any manner to get that, because neither of them is profit, right? You have to get the profit first: 16 - 11 = 5 profit.

Profit and loss is figured on the cost. So from here you follow the above pattern. You're wanting profit as a percent of cost. So divide in order: profit/cost.

Yes you already have that one right. I'm just trying to stress the concept behind it so that you can apply it to other things when you see them. And, well forgive me, but I kind of have a hangup about that. :)

[morgaine300]

OK, I'm done, finally.