Forgetful Fran

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					                                     Forgetful Fran
                                      Tina Roberts

Forgetful Fran loaned three friends a total of $127. All she can remember is that she
loaned the second friend $5 more than the first and the third friend twice as much as the
second. How much did she loan each friend?

When I first began to work out this problem, my initial idea was to use paper and pencil.
Then, I remembered that I could make my work so much easier if I chose to try Excel. I
knew Fran loaned $127 to three friends. Fran loaned one friend x amount, another friend
y=x+$5 more, and a third friend z=2y, which was twice as much as the second friend.

I made a column in Excel for friend 1 (any number x), a column for friend 2 (=a2+5), a
column for friend 3 (=b2*2), and a total column (=a2+b2+c2). I plugged in consecutive
numbers for column 1, starting with the number 1, 2, 3,…. I used consecutive numbers
for column 2, starting with the numbers 6, 7, 8…. Then I used 12 and 14 to start column
3. I highlighted the two answers per column and drug the mouse down so I would
complete the Excel chart using the formulas I had created. I then looked in the total
column to find 127, which was the total amount Fran loaned her friends all together. I
took the numbers 28, 33, and 66 as my final answer because they gave me a total of 127
in the Excel chart I created. (see attached)

A possible extension for this problem could be to use another amount that Fran loaned
her friends and figure out how much each friend was loaned. For example you could say
Fran loaned her friends a total of $175, how much did she loan each friend, under the
same stipulations as above? Or, you could give the amount Fran loaned one of the
friends to find how much she loaned the other two friends and then find the total amount
she loaned all of them together. For example, if she loaned friend 2 $20, how much
would she have loaned friend 1 and 3 and what is the total amount she loaned all