Math problem that I'm having a bit of difficulty
October 1, 2011 9:33pm CST
I received this problem for my math class and I'm having difficulty on where to start with figuring out a solution for the problem as well as the general problem. I'll put down everything that is required of me followed by the question itself. If anyone can help that would be great and even if it's just a starting point that's also helpful. I need to include the following: * A solution to the problem and the general problem. * Multiple extensions of the problem designed for elementary school classrooms. * Multiple modifications of the problem designed for elementary school classrooms. The question: At a carnival, players are to guess the weight of three objects; a tetrahedron, a sphere, and a cube. Players are given three different combinations of these items on scales. On scale #1, there is a tetrahedron, a cube, and a sphere. The weight displayed on the first scale is 23 kg. On scale #2, there are two cubes and two spheres. The weight displayed on the second scale is 22 kg. On scale #3, there are two tetrahedra, and one sphere. The weight displayed on the third scale is 26 kg. Determine the weights of the items, and explain how you could solve this problem algebraically. Use equations to describe the combinations of weights on each scale. Like I said, any help is help to me. I thought I could figure it out, but I'm so stumped on where to start with how to figure it out. I'm sure it's a simple equation but it's difficult for me to figure that part out!
• Kiryat Ata, Israel
2 Oct 11
the general solution will be with 3 general numbers as the informations about the sum of weights. t1 , t2 and t3 are the unknown numbers. and there are 3 equations that describe some information : 1)t1+t2+t3 = sum1 where sum1 is a given number 2)2t2+2t3 = sum2 , sum2 is also a given number 3)2t1+t3 = sum3 , sum3 is a given number the general solution will be some steps to describe t1 in terms of the other parts like t2 , t3 , sum1 , sum2 , sum3 The general solution is to isolate somehow t1 , writing t1 in terms of other informations other than t1. For example , one can think from sections 1) and 2) that t1 = sum1 - (sum2)/2 that's because (sum2)/2 = t2+t3 (one can conclude it fron section 2)... now , section 3 is the equation 2t1+t3 = sum3 , so it is actually says , 2sum1-sum2 + t3 = sum3 (that's because t1 = sum1-(sum2)/2 so 2t1 = 2sum1-sum2 ) so t3= sum3-2sum1+sum2 the finall step will be to delet t3 from section 2 and write "sum3-2sum1+sum2" instead of t3. and then just to isolate t2 and that's it. now , from section 2 we can figure out that t2= (sum2)/2 -t3 that is (sum2)/2 - sum3+2sum1-sum2 that is t2= -(sum2)/2-sum3+2sum1 that's a dirty work but it is technical and needs some attention to aviod mistakes with "+" and "-" lol. Next time , if you get a similar problem but with real numbers instead of sum1, sum2,sum3 , you can just use the general solutions.
1 person likes this
• Kiryat Ata, Israel
3 Oct 11
I guess she is a young girl so she doesn't learn Linear algebra in the academy. Equations system is the basic of Linear algebra so I realized that the general solution for her level would be only 3 variables with 3 equations with the same factors. The real general question would be 3 equations with 3 variables multiplied by general factors : a11*t1+a12*t2+a13*t3=S1 a21*t1+a22*t2+a23*t3=S2 a31*t1+a32*t2+a33*t3=S3
2 Oct 11
I didn't understand all of your problem. The itens 2 and 3 don't make sense to me, as I really don't know what are you studying. With you explain me better, maybe I can help you. About the item 1, I can help you with the solution for the problem, but what do you mean with "the general problem"? You can easily solve this problem just substituting the weights of the items for lettes. So, in the equations x = tetrahedron weight, y = cube weight and z = sphere weight. With you read the problem with attention you will find this equations (the solution in on sequence too): x + y + z = 23 (1) 2y + 2z = 22 - y = 11 - z (2) 2x + z = 26 - x = 13 - z/2 (3) substituting (2) and (3) on equation (1): (13 - z/2) + (11 - z) + z = 23 24 - z/2 = 23 z = 2 substituting z on (2) and (3): y = 9 x = 12 If you don't understand something, ask me. And try to explain better to get more help. In time, I think the problem in Brazil would be made people do something in carnival hehe. Happy mylotting and good luck.
• United States
2 Oct 11
Thank you so much for the help, I had my cousin help me come up with a solution and she basically came up with the same formulas you used. As far as the general solution goes I'm not entirely sure what my professor expects since that's all that was on the directions sheet. I'm going to look through old notes to see if I find something about a general problem but my guess is maybe saying if you have x amount of amounts on one said, how much will it weigh. That way there is a solution for the whole problem instead of individual scales like the scale #1, #2, #3 each having separate weights. Once again, thank you very much for your help!
2 Oct 11
@gabbymg You are welcome. That is not a difficult problem, as almost all problems in math the difficult is to find the equations that describes it. As I understand it, the general problem is a way to show the problem without numbers, do you understand? For example, the general problem for two itens would be (with x and y as the itens' weigth, r as the total weight and the letters with numbers as the coefficients) a1x + a2y = r1 b1x + b2y = r2 Without forget that you need as many equation as the amount of itens. Explain this to you cousin and maybe she can help you more. Happy mylotting. @chiumee Thanks. But I am not the only one who have capacity to solve this. Probably there are a lot people here who could help her, I was just the first one who saw it. Thanks again and keep studying. Happy mylotting.