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Math 1- Mathematics In the Modern World Use Polya's Four-step Problem Solving Strategy and the problem ~solving procedures t0 solve each of the following probl...

Question

Math 1- Mathematics In the Modern World Use Polya's Four-step Problem Solving Strategy and the problem ~solving procedures t0 solve each of the following problems: There are 364 first grade Students in Park Elementary School. If there areg6 more girls than boys, how many girls are there? A shirt ond tie together costs 50 dollars. The shirt costs 30 dollars more than the tie What is the cost of the shirt? If eight people greet each other at_ meeting by shaking hands with one another,how many

Math 1- Mathematics In the Modern World Use Polya's Four-step Problem Solving Strategy and the problem ~solving procedures t0 solve each of the following problems: There are 364 first grade Students in Park Elementary School. If there areg6 more girls than boys, how many girls are there? A shirt ond tie together costs 50 dollars. The shirt costs 30 dollars more than the tie What is the cost of the shirt? If eight people greet each other at_ meeting by shaking hands with one another,how many handshakes take place? How many squares are in the figure? room medsures 12 feet by 15 feet;How many ft.by 3 ft squares o1 carpet are needed t0 cover the floor of this room?



Answers

Solve the given problems by determinants. In Exercises $40-46,$ set up appropriate systems of equations. All numbers are accurate to at least two significant digits. An online retailer requires three different size containers to package its products for shipment. The costs of these containers, $A, B$ and $C$, and their capacities are shown as follows: $\begin{array}{lccc}\text { Container } & A & B & C \\ \text { cost (S each) } & 4 & 6 & 7 \\ \text { Capacity (in. }^{3} \text { ) } & 200 & 400 & 600\end{array}$ If the retailer orders 2500 containers with a total capacity of $1.1 \times 10^{6}$ in. $^{3}$ at a cost of $\$ 15,000,$ how many of each are in the order?

Let the number hats the X in the number four viscous on this Libby White according to the conditions given in the question for Stockport. Each unit all at Kew Pies. Yeah, a space off boom meter square on each unit. Officer, look the best form of squares, toe eggs, That's or why the local area must be less than equal 12 m school in the second condition is some got a lot reaction. This is this is sort of the less than equal, high near to maximize the number of enquiries. So enquiries for teaching the practice is three on using less tools. So we need Maximus He expressed to buy So no other food do type obviously and he's sort of bigger, but that he called to zero because they cannot be negative with my note. Maximum weirdly will not political. Okay, so this can result in a X morning six. That's why your home tree? Yes, in accordance one discovered minutes upon by where you can find one. So physical, six comma, zero device. So you're from a tree so lying over this and when this is by and this despite on this evil, she's lying, representing X That's why less than a goto life will be this on the favorable reason will be all the points delivered up heroes all the ones below that card. So our uh huh, Ariel, he's evil. So listen in this for critical. So we know the points. This is zero comma zero is zero for three. This is, like almost settle on this point for this street on vote. Absolutely. There we can substitute one of the variables into the other equation. So go into five minutes. Expressed board. Right Is able to do that. School school Home Minister to prove I has a photo of Isaac one accessible before. So this point is for coma warm. We checked the value or the monks and she expressed tow her case. Four points snap, Eric zero comma tree She do zero plus tau put two years ago. Six. Heck, aceto, almost zero three into zero Stone zero visibility. Eric who won with three and go to school into one visible 14. And that, uh huh, by Hamas hero to do like that's two Windows 00 52. The maximum value is obtain that by almost zero the maximum galleries bean So therefore, the number off hearts. His wife, in essence, is it going to zero on next year on the value of inquiry is with me.

Here in this question we've seen provided some information regarding the price off an item on the amount of actively. Okay, so basically, over here, there is an equation involved. That is why is equal to 0.95 times X there X is the price often item, or you can sell a product on. Why is the amount of tax that has to be paid? Okay, so amount off tax to be paid. Now, we're starting with the first part over here. You simply have to complete the people. I was giving the cushion and just write that in the form of ordered it. So the paper that has been giving, uh, being provided the values off X over here and excess What X is basically the price, often items. So that means we've been provided the information regarding the price Often. Item on. We simply have to find out the culture in tax that has toe page each and paper. So just I'm just coping. Though you can see the fries tonight on the X coordinates, then correspondingly kind of the values off. There are four values giving to us over here. Yeah, no table is now today. Now, for the first case, we've been forgiven the value off excess 100. So to find out the corresponding value of 51 I'm going to do is I'm just going to put X equals 100 in the equation off. Why? Equal to 0.95 So just put that put X equal 200 over a day, we'll get the corresponding value off. Why as bicycle to 0.95 times 100. So this would be equal toe 9.5, right? Just keep writing it over here and the table. Similarly, when X is equal to 1, 4100 and 40 then why will be equal to 0.95 times 1 40 so that will be equal to 13.30 Similarly, when X is equal to 210.72 then why will be equal to 0.95 times 210.72 on? If you just multiply this, you'll get 20.184 Looking for any 0.184 on the last case is when X is equal to 250. Then why will be equal to 0.95 times 250. So that will be equal to 23.75 So now you can see that the table is company Now, as it was already said, that we just have to write this in the form of ordered pays. So the first ordered paper tea 100 0.0 Spiegel coma nine point. Okay, the second off table B 140.0 Comma the bike owner, that is 13.30 The fourth one is 210.72 on the Y. Coordinate is 20.184 on the last one is 250 the corresponding by coordinators 23 point 75 So this is about a Patrick now, now moving on to the part. What do you have to do? Is we just have to grab this ordered pairs over here? I'm just nosiness toe and say cornet system, and I'm just going to applaud these ordered days over here on the ground. So let's say this is but the right now people find B is with you. So the first order Paris 100.0 Arizona explain. So it will be over here on the X axis. And the response value is 9.5. So I'm going toe move. So off word Palito the Y axis. So see, this is 100. Oh, coma 9.5. The second order. Paris. 140 And on the exact is and the corresponding bygone. Ages 13.30 So it will be over here, Right? This is 140.0 13.30 The next one is 210.72 on the responding. Why corn? It is 20.184 So you can see it will lie over here. So 210.72 on 20.184 The last one is 250 the corresponding by quantities 23.75 So were you. This one is what this will be 250.0 by coordinators 23.75 So, as you can see over here, I'm just marked all the ordered based on the craft. So the be part is also company. Let's move it. We don't see part embassy party being asked that. What does the order to pay? 140.0 13 countries zero represent over here according to the giving information. So let's see. Mhm. Okay. See, if you just look over here, e cannot go see. Let me just write it with you. Yeah, so does see pant moving here. Let's try to see part over here. So the given ordered pair is 140 0.0 Homa 13.30 So, as you can see, the X coordinate was representing though price often item on the Y coordinate was representing the amount of tax that has to be paid So simply, it is clear that this ordered paid to prisons that if we're built totals $140. Then the serious tax will be 3 $13.30. So I can see that it though, Bill, if the build amounts toe 140 dollars, then the sales tax will be been me $13.30. So this is about BC part Do we want to the deep part now Day party saying how much path with a customer if the cost off night? Um, it's 208.7 The cost of an item that means X over here. So the value of X is given to us as 200 thin right x coordinate at exactly $110.72. So the corresponding why value will be what why is equal to the equation was already given to us 0.0 in five game six. So through this value off exit the question. So you 0.95 aims to 10 10.72 If you just multiply, you will get 20.2 on. Since this is the price or the task that has to be a place hence so unit will be dollars. So that means $20.2 has to be paid for it. I had cost 203.72 writers, no coming on he part of the hill. So the impact is to defend the graph on do you observe any faction indicated by the 0.2 years. All these points are lying on a straight line. If you will see, see if you just joined them. No, you'll get a straight line. Let's do that. I'll do it with a different color. Okay, So, see, see if you are joining them. It is forming a straight line, isn't it? So the pattern that you can observe is that all the points over here on language in a straight line. So although points lie on Wall Street line also, you can see that as the price of an item is increasing toward tax paid is also increasing right now, moving on to those he asked part. I suppose it is the last market. So the question is saying that if a customer has played $19 Oh, as a tax, then what was the cost of the item police. So we're here giving you the value off by the fact over here the indicated by the Y coordinate. So the value of y is given to a sense nine values. So we have to find out the corresponding value off it. So for that, what I'm going toe, um, again, just going to shoot the value off X, giving a question that was is equal to you. 0.98 times X. Now, if you just divide Bhutto's aides off the equation, 0.9 I will get the value off X so X is equal to $200. So the answer is that if your finger tax off $19 that means the item purchased cost $200. So this is how you just answer off problem, or you can say, uh, questions based on grass or some information that is given to you.

All right, everyone in this person, you will find that 11 of big before were given. It demanded, all so divided by explicit. So I think you demanded they didn't work between Diet Cola. Normally for go, it's divided people normal by explicitly or any divided then or red with first person less, not less, into bless the opportunity right there. Let's remember. So this is a former one for normal. If you deny this for normal buying divided then for normal bullet again, I questioned into the right place so very fair play. Then we open support really dead your face is that for change? So that person, you don't know the effect Is that the right to the evidence given explicit E? But this is simply explicit. E less demand raised doing who now about question. There is no important missing on the only the one for normal degrees for so here exported one already reality. But here the grieving victory then only will get today and to one degree four with admits percent will help the military. So we can I don't people normal off dignity and people American, a Jew because they did not understand about this question. So if I assumed that what I did tonight Texas Excuse last the nexus play Blessed be X. Let's be and do a Plessy. Let's do this is a require for London of degree for when we look. Reddish them through this time and get the report. So let's simplify the opposite Bordeaux. This in bodies, the extra part for less the extra power less big. Spread the e eggs. Let's see. Then it's next to you. Let's just play. Bless you now for benefits and bread into your accident. Ready for you the next bar four. Unless it's you, that is a problem here, then be less. You see its yield less predicted to Stratasys football. My more depress using Intuit's fled. Actually, if you did it for one, then they get eat less. Do they do it? You see less so the sport litigated. So this is for London on legally for a potential new, uninformed person. So about a B B, they don't know how we can find they do maybe the whole time before they did not understand about discussions, so they're really not fine. So four they live a long and did reveal are the lumber. Glad for London is advances like before for London and you

Now over here. In this question, it has been already stated that the cost off each tape is $0.40. So I'm just writing that as it is, because off for each tape is $0.40 fine. Another thing that has given us the weekly fixed cost so that the weekly fix course that is already specified towards this $10,000 weekly fix courses will too $10,000. Right now, what is being asked first were young. Apart from that, we've been giving the selling price also. So I am just denoting that as S P over here, the selling price off each tape is $2. Fine. Now you just have to find out the number off tapes that should be produced on sold in a week in order to make up profit. So for profit, what do we know? Profit is always made When S P is greater than CPI. The selling price is greater than the cost price, right? So, yeah, Whenever the SP becomes written in the selling price, we think you're a profit. Now let us start by as humane eggs as the number of tape that is produced and sold each week. Spine exist them number Oh, tapes produced and sold in a week. So, as I see a profit will be yeah, made when it speeds greater than the c P s pieces already given to us us to on that it's poor tape. The selling price eyes $2. 40. That means for X days it will be two weeks on SP should be greater than CPI. As I say, CPS what CPI will be the weekly fixed cost president cause poor tape Weekly fixed causes 10,000 on Because poor tape is 0.40 x For ex tapes, it will be 0.40 x for one tape, it is 0.46 state for X tapes, it will be 0.40 x. So now the inequality has been framed. We just need to solve for the value off X. So how do we solve for the value of X? Simply Just bring the constants on one side and the variables on the adult. So now two x minus 0.40 x That will give you 1.60 X, isn't it? And that should be greater than 10 housing now, the soul, the value off eggs. For that, we just need to divine what decides by 1.60 So if you just divide 10,000 by 1.60 you'll be getting 6250. So over here, X is greater than 6250. Hence more than 6000 250 tapes should be produced on sold in order to make er profit. I think this was a very simple one, just the basic concept. We should all know that profit is always me whenever the selling price is greater than the cost price.


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