BTW if you know of any books that actually teach one how to do problems like these, please let me know. I have a hard time quantifying these problems into algebra. The book shows some easy ones and then throws this crap at you in the problems section. I don't need help with the algebra. I just need a way to set up these problems and other word problems. It gets pretty old after a while seeing problems that the book never teaches you how to do. the problems are show in the attachments. the first (number 81) i really don't even know where to begin. I see what the book did and don't trust it. (how did they get to 150+x and 200-x ? I can understand multiplying x of boxes times price per box, but quantifying those two things is currently beyond me). as for the second one (number 83), where did they come up with the number 27? the volume is 1 cubic foot. that's 36 cubic inches IIRC.
#81, as a start, the unknown is the number of boxes bought, x. You are given pricing information. Analyze the information and make the proper expressions and equations; and solve for the number of boxes which were bought. More help after you have tried this. Is this set of exercises from an Intermediate Algebra book?
I had already tried both of these. on 81 i came up with (200x)-(150x) which wouldn't be close. the problem is that 200x works up until i hit 151 boxes. from then on the cost per box is reduced in dollars x equal to x number of boxes made after 150 boxes. i have no idea how to put that into the equation. I really have no idea how to construct such problems. and it is from a college algebra book. and did i give up too soon on 83? should i have just changed the 27 to a 36?
Sorry, Curd, I briefly looked at your answer solution key after I gave my comment but did not yet work the solution myself. The key for #81 appeared fairly/very good, what I might well expect. What I said, maybe not specific enough is still generally how one would go about solving. Those two #81 and #83 look like typical application exercises for Intermediate Algebra.
okay... So, how did they come up with what they came up with for #81 (mostly the 150+x and the 200-x) and where did they get the number 27 for #83?
Getting problems like these set up correctly is usually the hard part, and solving the resulting equations is often much easier. The volume of concrete is 1 cubic yard, which is 27 cubic feet.
i know. so, how and why was #81 set up the way it was set up? and is there any sort of method for setting up these problems?
It's basically a matter of translating the words into equations. In this problem you are indirectly given that the customer ordered more than 150 boxes, since the cost was $30,525. We know that the customer ordered more than 150 boxes, since an order of 150 boxes would cost $30,000. Let x = the number of boxes over 150 Then total boxes ordered = x + 150 If x + 150 boxes are ordered, and the cost of each is 200 - x, what's the cost of this order?
i think i see 200 minus the the cost of the boxes which reduces by the number of boxes sold (for each box) and since we're already over 150 boxes i don't have to bother with setting a limit at which the pricing process changes. now, how would the equation be made if instead the first 150 boxes were 200 and then after that we started changing the price with the previous method stated? would we just add 150*200 to the equation?
No, not 200 - the cost of the boxes. It's 200 - the number of boxes over 150. For example, if the order happened to be for 180 boxes, then x = 30, and the per-box cost is 200 - 30 = 170 dollars. You need to be clearer in what you're asking. I don't know what you mean by "if instead the first 150 boxes were 200". Are you asking how the problem would be different if the first 200 boxes cost $200 each, but for an order over 200 boxes, the per-unit cost would be 200 - x?
i'm not even sure how to word what i'm asking. my mind is flooded at the moment so i think i'll hold off on this until tomorrow.
After examing the solution key for #83, it makes perfect sense. Curd, are you still confused about this one? Total area is variable; then subtraction of the garden's area to get area of just the border; then multiplied by known and given 3 inches (equal to 0.25 feet), to get expression for VOLUME of the premix cement. You are also given the value for volume of premix cement.
yeah, 83 makes sense to me now to. i just needed to make sure to convert all the units into the same type... that and make sure that i put x's where i meant to. 81 is the only one that's really bugging me anymore although i have about 6 problems to go so this may change. could one of you explain in EXTREME detail the reasoning behind the conversion of the #81 word problem into algebraic form? I think i understand why they got (200-x) which correlates to the part where if the cost of x boxes if the order is more than 150 boxes then each box ordered is reduced (reduced meaning minus, not divide or anything like that) by x dollars. i don't really understand why they came up with the (150+x). why not just have (200-x)x instead of (200-x)(150+x)? after all, at the end of the problem, the way they did it, you have to add back in the 150. also i have a problem understand which one of these below set ups it relevant to the actual problem 1) if you go past 150 boxes then each and ALL boxes x ordered are reduced reduced by x dollars in price 2) if you go past 150 boxes then each box PAST the 150th box is reduced x dollars for x boxes PAST 150 boxes. please clarify all of this.
Because of how they defined x, which was the number of boxes over 150. This means that the total number of boxes is 150 + x. This is explicitly stated in the first two lines in the answer. x is not the total number of boxes ordered, as I already said above. If you order more than 150 boxes, all boxes are reduced in price by x dollars. No, this isn't what the problem is saying.
yes, but it didn't say that x was that in the problem. could this be calculated with x instead of 150+x? are there other ways this problem could be done? i keep thinking if i saw it done another way it may make more sense to me.
Yes they did. "If a customer orders x boxes in excess of 150..." They are pretty much telling you what x should represent, and that's the way the solution is laid out. Of course. You can define x to mean whatever you want, but it will affect all the other calculations. You have the problem and you have their solution laid out in a very natural way. Rather than giving up so easily at trying to understand what they're doing, it makes more sense to me to try harder to understand what is right there before you. What is it that doesn't make sense to you?
sometimes pictures aren't clear from one perspective. sometimes you have to see them from other angles. so, basically i wasn't giving up, i was just asking you to solve it a different ways so that i could see how those ways relate to the way the book had done the problem. you can repeat that the book said such and such over and over again, and i've looked at it over and over again already, but that is not going to get me anywhere. when one avenue is hard to see down, try another, they are all leading to the same place. please provide an avenue which is accurate so that i may get to the destination i wish to. trying to understand something is not a process of merely looking at the same thing that befuddles you from the same perspective. that's a waste of time if you have already been doing it and it makes no sense to continue doing the same thing that fails. the best thing to do is look at the problem from many perspectives, in that case, then look at each perspective, how they relate to each other and the problem and hopefully gain understanding from that.... i think that's the best way to say what i was trying to. so, please show me other way to do the problem and perhaps i will be able to understand it. also, if we're already assuming that each box's price is effect by (200-x), then what do we need the 150 for? wouldn't leaving out the 150 + from (150+x), and just having x, give us the answer without having to add back in the 150?
You said, I replied, I think that the problem might be that you haven't worked this problem at all, together with the fact that you are unable to follow the book's solution. The best way for you to understand this problem is to tackle it yourself, and do it in some way that makes sense to you. As I said before, you can define the variable x to be anything you want, so x = the number of boxes ordered. What expression represents the cost per box? You'll have to take into account that if x > 150, the per-unit cost is less. You know how much the total order is, so what is your equation that represents that order?
Rethinking the problem description can help you understand it clearer. The reduced rate of 200-x is applied to ALL of the boxes; if customer buys more than 150 boxes, then he is buying 150+x boxes.
Another important basic approach is to remind yourself to use the fundamental formula for Cost: Cost equals Price multiplied by Units. Sometimes people forget to look for fundamental concepts, and determine needed expressions for the numbers of the fundamental formulas.