#$&* course Mth 158 6/27 5 pm 5 + x = .40 ( 20 + x ). After the distributive law we have
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Given Solution: * * Solution from Previous Student and Instructor Comment: It's not possible, adding a 25% solution to a 48% solution is only going to dilute it, I don't really know how to prove that algebraically, but logically that's what I think. (This is much like the last problem, that I don't really understand). INSTRUCTOR COMMENT: Right but the 48% solution is being added to the 25% solution. Correct statement, mostly in your words Adding a 48% solution to a 25% solution will never give you a 58% solution. Both concentrations are less than the desired concentration. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): okay that was a lot simpler than I thought it was supposed to be. ------------------------------------------------ Self-critique Rating: ok ********************************************* Additional student questions related to setting up 'word problems': A total of $20,000 is to be invested, some in bonds and some in certificates of deposit (CD's). If the amount invested in bonds is to exceed that in CDs by $3,000, how much will be invested in each type of investment? I thought about it and took the 20,000 and divided it by 2 giving me $10,000 each. I subtracted 3,000 from 10,000 and that gave me 7,000 for one and 10,000 for the other, but that's not enough, so the remaining $3,000 I divided by 2 and added 1,500 to each amount. I came up with $8,500 for one and $11,500 for the other. I know this is the right answer, but how do you set it up in a formula? If you know how much is invested in bonds, then what arithmetic operation do you perform to get the amount invested in CDs? Let x stand for the amount invested in bonds. Then, using the arithmetic operation of your answer to the first question, how much is invested in CDs? You should now have two expressions, both involving x, one representing the amount invested in CDs and the other the amount invested in bonds. If you are given two numbers, then what calculation do you do to see if the second is $3000 greater than the first? If the amounts of the investments are represented by your two expressions (in terms of x), then what expression represents this calculation? If you set this expression equal to $3000, you get an equation with variable x. Solve it for x. What do you get? Give me your best answers to these questions and I'll be glad to give you feedback. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Additional student questions related to setting up 'word problems': A total of $20,000 is to be invested, some in bonds and some in certificates of deposit (CD's). If the amount invested in bonds is to exceed that in CDs by $3,000, how much will be invested in each type of investment? I thought about it and took the 20,000 and divided it by 2 giving me $10,000 each. I subtracted 3,000 from 10,000 and that gave me 7,000 for one and 10,000 for the other, but that's not enough, so the remaining $3,000 I divided by 2 and added 1,500 to each amount. I came up with $8,500 for one and $11,500 for the other. I know this is the right answer, but how do you set it up in a formula? If you know how much is invested in bonds, then what arithmetic operation do you perform to get the amount invested in CDs? Let x stand for the amount invested in bonds. Then, using the arithmetic operation of your answer to the first question, how much is invested in CDs? You should now have two expressions, both involving x, one representing the amount invested in CDs and the other the amount invested in bonds. If you are given two numbers, then what calculation do you do to see if the second is $3000 greater than the first? If the amounts of the investments are represented by your two expressions (in terms of x), then what expression represents this calculation? If you set this expression equal to $3000, you get an equation with variable x. Solve it for x. What do you get? Give me your best answers to these questions and I'll be glad to give you feedback. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&! ********************************************* Additional student questions related to setting up 'word problems': A total of $20,000 is to be invested, some in bonds and some in certificates of deposit (CD's). If the amount invested in bonds is to exceed that in CDs by $3,000, how much will be invested in each type of investment? I thought about it and took the 20,000 and divided it by 2 giving me $10,000 each. I subtracted 3,000 from 10,000 and that gave me 7,000 for one and 10,000 for the other, but that's not enough, so the remaining $3,000 I divided by 2 and added 1,500 to each amount. I came up with $8,500 for one and $11,500 for the other. I know this is the right answer, but how do you set it up in a formula? If you know how much is invested in bonds, then what arithmetic operation do you perform to get the amount invested in CDs? Let x stand for the amount invested in bonds. Then, using the arithmetic operation of your answer to the first question, how much is invested in CDs? You should now have two expressions, both involving x, one representing the amount invested in CDs and the other the amount invested in bonds. If you are given two numbers, then what calculation do you do to see if the second is $3000 greater than the first? If the amounts of the investments are represented by your two expressions (in terms of x), then what expression represents this calculation? If you set this expression equal to $3000, you get an equation with variable x. Solve it for x. What do you get? Give me your best answers to these questions and I'll be glad to give you feedback. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!#*&!