Problem Statement:
An absent minded teller switched the dollars and cents when she cashed a check for someone. She gave him dollars instead of cents and cents instead of dollars. Only after he bought a .05 cent newspaper that he realized that he twice as much as his original check. Find the amount of the check. Process: Step 1) I decided that x=the amount on the check and y=the amount hes given. Then my group and I decided on the equation y=(x-.05)2. The rest of the class also came up with equations and once everyone had their equations, as a class we started to list what they had in common and pick out the ones that wouldn’t work. Step 2) After we picked out the ones that didn’t work we decided that y-.05=2x. Then we got to the point to where we had to take into account the fact that the dollars and the cents were switched. Step 3) We decided that d=dollars and c=cents. To create an equation where the dollars and cents were switched we had to decide that y=d+c/100 and x=c+d/100. Then we plugged x and y into the equation. This made an extremely long equation that looked like (c+/100-5=2(d+2c/100) Then we multiplied each side by 100 and got 100c+d=200d+2c. After that we put all the c’s and d’s on separate sides and got d=98c-5/199. Step 4) I began plugging in answers and finally got the solution of $ 35.60 |
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