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## Share and Share Alike

When Karen inherited an amount of money, she divided it amongst her four children in the following sequence. To Alice, she game \$2 plus 1/3 of the remainder; to Brent, she game \$2 plus 1/3 of the new remainder; to Curtis, she game \$2 plus 1/3 of the new remainder; and finally to Debra, she game \$2 plus 1/3 of the new remainder. Karen then divided what was left equally amongst the four children. At the end, she discovered that the two girls together had received \$35 more than the boys together.

Questions: What was Karen's inheritance? How much money did each child receive?

If you are up to a harder task: When Karen inherited an amount of money, she divided it amongst her four children in the following sequence. To Alice, she game \$n plus 1/m of the remainder; to Brent, she game \$n plus 1/m of the new remainder; to Curtis, she game \$n plus 1/m of the new remainder; and finally to Debra, she game \$n plus 1/m of the new remainder. Karen then divided what was left equally amongst the four children. At the end, she discovered that the two girls together had received \$p more than the boys together.

Can you determine a general expression for Karen's inheritance and how much money each child received...and what if there were q childrfen, half of each sex?

Source: W. Fleming's College Algebra, 1988, p. 95

Hint: Life will get quite complicated if you set x to be Karen's original amount and then you try to set up algebraic equations for each step...try to think what other problem solving techniques might prove helpful.

Solution Commentary: You will know when you have the correct solution...so let's focus on technique. Did you discover that this was a good problem for working backwards...or even guess and check...or even playing with on a spreadsheet? Some great patterns are lurking within.... For example, if you assume that Karen had \$0 after giving Debra her share, you should be able to quickly figure out the original amount....plus certain numbers keep occurring.