smacker124 Posted November 18, 2003 Share Posted November 18, 2003 Okay, I know I got close to this but then I am not sure. Any help is appreciated: Here is the problem: There is a string of pearls, which has 33 pearls on it. The largest and most expensive one is in the middle. The string of pearl is worth $65,000. Starting from one end, each pearl is worth $100 more than the one before, up to the middle. Starting from the other end, each pearl is worth $150 more than the one before, up to the middle. What is the value of the middle pearl? Link to comment Share on other sites More sharing options...
VendingMenace Posted November 18, 2003 Share Posted November 18, 2003 cool, well i don't really want to just give you the answer, but i will give you some help for your journey First off, don't let all the numbers and stuff scare you off, the porblem is essentailly an addition problem. We know this, becuase when the value of all the pearls is added together, we must get the total value of the string. RIght? So, probably the best way to approach the problem is to randomly choose the value of one of the pearls and then discover the value of all the other perls in relation to this one. Cool, lets get started then. Well, from the problem we know that if we start at the middle pearl and move to one side, lets say the right, then the next pearl will be worth $100 less than the middle pearl. The next pearl again will be worth $200 less than the middle pearl and so on until we reach the last pearl in the chain. All in all, after the first pearl we find that there are 16 pearls till the end of the chain, so we have for those 16 pearls, the following, if we arbitrarily set the value of the middle pearl as "x"... (x-100) + (x-200) + ... + (x-1600) so that is the value of the right side of the pearls, not including the middle pearl, right? OK, the same proceedure can be used to find the value of the other side of the necklace (the left side in this case), not including the middle pearl. Cool, so after you get this you will have the value of the right side of the necklace, not including teh middle pearl and the value of the left side of the necklace, not including the middle pearl. All that is left is to add up these two values and the value of the middle pearl. This sum should equal the total value of the necklace, in this case $65,000. That is; (value of right side) + (value of left side) + (value of middle pearl) = (total value of necklace) well, that is how i would solve it. There are shorter ways of writting all this out, but i don't know if you know what a summation sign is :/ But hopefully that helps, if you have more questions, just ask. Have fun! Link to comment Share on other sites More sharing options...
Sayonara Posted November 18, 2003 Share Posted November 18, 2003 $65k is a lot to pay for a pearl necklace. Link to comment Share on other sites More sharing options...
Squintz Posted November 18, 2003 Share Posted November 18, 2003 Not only would it be an expensive necklace but it would also be funny looking. Never the less without knowing the price of atleast one pearl their is no numerical answer. Only an equation which makes the twister no fun for me to try and solve. I hate never getting the answer. Link to comment Share on other sites More sharing options...
VendingMenace Posted November 18, 2003 Share Posted November 18, 2003 there is a numerical answer. go through my method, you will find that you have one equation in the end and only one unknown (the price of the middle pearl). You may then solve for the price of the middle pearl. Link to comment Share on other sites More sharing options...
Squintz Posted November 18, 2003 Share Posted November 18, 2003 I dont understand how. Both sides dont have to start with the same valued first pearl. i could have. 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 -------------- 13.6K 2300 2150 2100 1950 1800 1650 1500 1350 1200 1050 900 750 600 450 300 150 ---------- 20.2k 13.6k + 20.2k = 33.8k 65k - 33.8k = 31.2k That math is true if the first pearl on each side starts at its incrementing number. 100 for the first side and 150 for the second side. The word problem does not state the value of the first pearl on either side nor does it state the value of any pearl in the whole necklace so where is the refrence point at which you start adding and subtracting. You cant just pick a random number and add 150 to it because your are then guessing. And it says add 150 an 100 up to the middle perl. I does not say including the middle pearl. and if you did include the middle pearl for each side of the necklace then the middle pearl would be 250 more than its previous pearl. So i don think this can be solved. Im sure it could be solved with variable and put into equation form. Link to comment Share on other sites More sharing options...
Duke Posted November 18, 2003 Share Posted November 18, 2003 yeah thats what i got. could be anything. but if you go up portmouth arcade, you can get a plastic pearl necklace for like, 20p and a robotic parrot gives it to you in an egg. Everybodies happy. Link to comment Share on other sites More sharing options...
Squintz Posted November 18, 2003 Share Posted November 18, 2003 Lets change it to a diamond necklace. It might be easier to imagine Link to comment Share on other sites More sharing options...
Duke Posted November 18, 2003 Share Posted November 18, 2003 if the first pearl on one side was 100 and the other 150 then i get about $48500 for the middle pearl. but its probably wrong cos i rushed the working out... so ignor me Link to comment Share on other sites More sharing options...
Squintz Posted November 18, 2003 Share Posted November 18, 2003 Well if the question is.... What is the value of the middle pearl? Then it can only be 2 answers with the given information 1) Not enough info 2) Some equation which im to lazy to work out. Unless its a trick question and there is some wording in the question that im just not picking up on. VendingMenace can you work out the problem for us? Link to comment Share on other sites More sharing options...
smacker124 Posted November 18, 2003 Author Share Posted November 18, 2003 The following is what I have: left side(100x) : 13,600 right side(150x) : 20,400 Total: 34,000 Misc. 65,000 - 34,000 = 31, 000 is that right? (according to VendingMenace's equtation up there) So the middle pearl's value is 31,000 ? Did I make any errors in my math? Squintz, I think there is a little error with your 150x column, you forgot to add on top of 2100 an additional 150 but just added an additional 50 2150 2100 Corrected: 2100, 2250, then 2400 Another question I have, since it doesn't give the start numbers on either side. For all you know it started at 200 (100x) and 300(150x) rather then themselves....Would lead to different middle value. This is a tricky problem I guess. Anyone here have a solution to this? An equtation perhaps? Cause I think most likly it requires an equtation since there are variables. Link to comment Share on other sites More sharing options...
VendingMenace Posted November 18, 2003 Share Posted November 18, 2003 The word problem does not state the value of the first pearl on either side nor does it state the value of any pearl in the whole necklace so where is the refrence point at which you start adding and subtracting. Well, my method is based on the fact that no matter what side you approach the middle pearl from, it must always have the same value. Correct? So, if we assume that the value of the middle pearl is X, we know that the value of the pearl directly to one side of the middle pearl is (x-100) and that the pearl directly to the other side of the middle is (x-150). Using this information we can write an equation for the entire neckace, which we know the value of. Thus, we have 1 equation and 1 unknown -- this means a numerical solution must be possible. VendingMenace can you work out the problem for us? Sure, i will write it all up when i get home and post it for you guys to look at. That will prolly be in like another 3 or 4 hours, but i will do it. cool Link to comment Share on other sites More sharing options...
Squintz Posted November 19, 2003 Share Posted November 19, 2003 im sure an equation for finding the value of every pearl is possible but the question was What is the value of the middle pearl? So your method does not answer the question unless you consider the variable x to be a value. Your assuming that the value of the middle pearl will be given but it cant be given because that is the question Link to comment Share on other sites More sharing options...
wolfson Posted November 21, 2003 Share Posted November 21, 2003 wooow OTT this is NOT quadratics this is a simple A.P. so u need to use equations those great thing i will go through step by step Link to comment Share on other sites More sharing options...
Duke Posted November 21, 2003 Share Posted November 21, 2003 is the middle pearl worth $100 dollars more than the pearl on one side and $150 more than the one on the other side. If so, i think there is only one answer... but err, im too busy to tell you. Link to comment Share on other sites More sharing options...
wolfson Posted November 21, 2003 Share Posted November 21, 2003 LMAO @ DUKE Ok sorry for the delay ive had computer issues (all the time lol) SO the sum of 33 pearls is equal to $65000 So Step One: On the right hand side we will say after the first term (a1) the difference is an increasment of $100 each time until the midlle (16), And on the Left hand side we will use $150 increasments after the first term (a1).Call R-h side first term a1 and l-h side first term a2. Step Two: a1 = n - 1 x d1 a1 being first term of r-h side n being the total of terms of side a1 which is 16 d being the difference after a1 which is $100 so: a1 = 16 -1 x 100 = $1500 so the first term on r-h side is 1500 a2 = n - 1 x (d2 -d1) a2 being first term of l-h side n same as above d2 being diff after a2 ($150) d1 diff after a1 ($100) Bit different but easier than quadractics so: a2 = 16 - 1 x (150- 100) =$750 So the first term of left hand side = $750 Final step: for right hand side: middle term = n - 1 x d 1 + a1 = 16 -1 x 100 + 1500 = $3000 and solution for left hand side: middle term = n - 16 x d2 + a2 = 16 - 1 x 150 + 750 =$3000 The most expensive is $3000. Really you only have to do ONE side but im just showing both possibilites here. The long was is inappropriate. This is the best way to solve A.P. binomal equation, and you must learn o use them... i can show you a quadratic if you wish...and just email me or post for any other solutions....gl Link to comment Share on other sites More sharing options...
wolfson Posted November 21, 2003 Share Posted November 21, 2003 6 line 15 word (approx) left hand side is a2 NOT a1 sry for the error me v bad typing skills... Link to comment Share on other sites More sharing options...
VendingMenace Posted November 21, 2003 Share Posted November 21, 2003 cool, well it appears wolfson already posted a reply, but i had this ready to go too, so i will post it anyways. More explinations cannot help. And i think i got a different answer too, but mine could be wrong. well, sorry about this post, i will post images is just a bit Link to comment Share on other sites More sharing options...
Squintz Posted November 21, 2003 Share Posted November 21, 2003 i think im more confused now that i ever was. Link to comment Share on other sites More sharing options...
Squintz Posted November 21, 2003 Share Posted November 21, 2003 How about resizing those images Link to comment Share on other sites More sharing options...
VendingMenace Posted November 21, 2003 Share Posted November 21, 2003 ok, sorry about that other post, i have resized the images now and i will post them. I feel this is a fairly decent explination, i hope it is clear. Anyways, there are a total of three pages, so read them all, and feel free to ask questions on them. Well, without further ado, on with the first page. Link to comment Share on other sites More sharing options...
VendingMenace Posted November 21, 2003 Share Posted November 21, 2003 page 2, enjoy Link to comment Share on other sites More sharing options...
VendingMenace Posted November 21, 2003 Share Posted November 21, 2003 holy nut, sorry about this. last page to come hopefully someone will delete this post, i seem to be having problems with attachemnts, sorry (ps. scroll down to see the third page) Link to comment Share on other sites More sharing options...
Squintz Posted November 21, 2003 Share Posted November 21, 2003 Id enjoy it if i could see it. Page 3 is too small. How come you couldnt just post the text instead of scaning in the printed version. Link to comment Share on other sites More sharing options...
VendingMenace Posted November 21, 2003 Share Posted November 21, 2003 well, here is the grand finale, page 3. Hope it helps Link to comment Share on other sites More sharing options...
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