POW #13: The Absent-Minded Teller
Problem Statement:
An absent-minded teller switched the dollars and cents when she cashed a check for Mr. Brown, giving him dollars instead of cents and cents instead of dollars. After buying a five-cent newspaper, Brown discovered that he had exactly twice as much left as his original check. What was the amount of the check?
Process:
What I first did was read the question and tried to find an equation. The equation I got was y=2x+.05. X= The amount on the check. Y=The amount he is given. Each table group shared out there equation and then we wrote down some common characteristics. What some common characteristics for the equations were they all had 5 cents in them and a lot of them had multiply by two (he had twice as much). Each table group got assigned a equation to check if it would work. None of them worked so then we tried to find a new equation when D=Dollars C=Cents. What my group got was C.D-.05. One person from every group had to go write their equation on a whiteboard so another group can check if it works. My groups equation didn’t work but one persons group equation did. The equation they got was C+D/100. That was the equation we had for cents but then in in the problem statement it says that the Absent-Minded teller switched the dollars and cents. We had to come up with an equation for the dollars, what we did was just switched the variables. The equation for dollars was D+C/100. Also it says in the problem statement that Mr. Brown bought a five cent newspaper so we had to combine both of the equations and we got C+D/100-.05=2(D+C/100). We had to simplify it and what we did to simplify it was times 2 and D to make 2D+c/100. After that we subtracted the 100 from C/100 on both sides. What we ended up getting after that was 100C+D-5=200D+2C. What we did next was subtract 2C from each sides. After we subtracted that the equation was 98C+D-5=200D. Then after that we subtracted the one D from each side to get 98C-5=199D. Then we took the 199 and switched it to the other side and then it was D=98C-5/199. After that I got confused on what to do next but then Kenneth told me to make a google spreadsheet and put C in the first space in the A column and then started putting 2 in the 2 column and 3 in the 3 column and so on till 199. I put just the first few numbers in the A column and then tried to see if I can do something to get the numbers automatically all the way to 199 so I would have to type all of them in. Kenneth tried helping me with that but it wasn’t working so I just manually put them in. When I was finished Kenneth told me to put the equation (D=98C-5/199) in column C and then he told me solve the first couple of equations and enter the answers into column B and told me to try to get the answers for all of them by dragging the B column down to 199 but it didn’t work its just repeated the same answer. What I did since I couldn’t figure out out to use the google spreadsheet was write down the equation and plug in a numbers until I got the answer.
Problem Statement:
An absent-minded teller switched the dollars and cents when she cashed a check for Mr. Brown, giving him dollars instead of cents and cents instead of dollars. After buying a five-cent newspaper, Brown discovered that he had exactly twice as much left as his original check. What was the amount of the check?
Process:
What I first did was read the question and tried to find an equation. The equation I got was y=2x+.05. X= The amount on the check. Y=The amount he is given. Each table group shared out there equation and then we wrote down some common characteristics. What some common characteristics for the equations were they all had 5 cents in them and a lot of them had multiply by two (he had twice as much). Each table group got assigned a equation to check if it would work. None of them worked so then we tried to find a new equation when D=Dollars C=Cents. What my group got was C.D-.05. One person from every group had to go write their equation on a whiteboard so another group can check if it works. My groups equation didn’t work but one persons group equation did. The equation they got was C+D/100. That was the equation we had for cents but then in in the problem statement it says that the Absent-Minded teller switched the dollars and cents. We had to come up with an equation for the dollars, what we did was just switched the variables. The equation for dollars was D+C/100. Also it says in the problem statement that Mr. Brown bought a five cent newspaper so we had to combine both of the equations and we got C+D/100-.05=2(D+C/100). We had to simplify it and what we did to simplify it was times 2 and D to make 2D+c/100. After that we subtracted the 100 from C/100 on both sides. What we ended up getting after that was 100C+D-5=200D+2C. What we did next was subtract 2C from each sides. After we subtracted that the equation was 98C+D-5=200D. Then after that we subtracted the one D from each side to get 98C-5=199D. Then we took the 199 and switched it to the other side and then it was D=98C-5/199. After that I got confused on what to do next but then Kenneth told me to make a google spreadsheet and put C in the first space in the A column and then started putting 2 in the 2 column and 3 in the 3 column and so on till 199. I put just the first few numbers in the A column and then tried to see if I can do something to get the numbers automatically all the way to 199 so I would have to type all of them in. Kenneth tried helping me with that but it wasn’t working so I just manually put them in. When I was finished Kenneth told me to put the equation (D=98C-5/199) in column C and then he told me solve the first couple of equations and enter the answers into column B and told me to try to get the answers for all of them by dragging the B column down to 199 but it didn’t work its just repeated the same answer. What I did since I couldn’t figure out out to use the google spreadsheet was write down the equation and plug in a numbers until I got the answer.
Solution:
The solution I got was $31.63. I knew that was my answer when I did 98*63=6174-5=61669/199=31. Jocelyn told us that there is only one whole number and that whole number is the answer. I knew 63 was cents because thats what I plugged in with C.
Evaluation: I really didn’t like this problem but at the same time I did. I didn't like it because it was too difficult and confusing and I also didn’t like coming up with the equations. What I liked was writing out each equation and plugging in different numbers, it took a long time but I did enjoy doing that. Overall I wouldn’t want to see problems like this in the future it was too challenging.
The solution I got was $31.63. I knew that was my answer when I did 98*63=6174-5=61669/199=31. Jocelyn told us that there is only one whole number and that whole number is the answer. I knew 63 was cents because thats what I plugged in with C.
Evaluation: I really didn’t like this problem but at the same time I did. I didn't like it because it was too difficult and confusing and I also didn’t like coming up with the equations. What I liked was writing out each equation and plugging in different numbers, it took a long time but I did enjoy doing that. Overall I wouldn’t want to see problems like this in the future it was too challenging.