Learning Resources

Investigation 2: Cutting Down on Empty Calories

Step E

Once you have completed the table, add all the values in column 1 (Carl's total). You should get a total of 1289.84375 which is exactly double the difference between Carl's first amount and Wendy's last amount.  You may find it easier to write this another way, as illustrated below.

Let S represent the amount of pop Carl drank. We can now write:

                S = 650 + 325 + 162.5 + ... + 10.156 25

Thus:   S = 325 +  162.5 + ... + 10.156 25 + 5.078 125

We can subtract the equations to get: S = 650 - 5.078 125

Solving for S, we get:                                S = 2(650 - 5.078 125) 

This value for S, the amount of pop Carl drank, is clearly double the difference between Carl's first amount and Wendy's last amount.