algebra

i was at my parents' place last night and my nephew approached me for help in his homework.  ok.  ooops... algebra.  i was president of math club in high school but now i don't even know how to add, ugh!

some of the answers i knew instinctively, like, 50% of what number is 15?  easy.  30.  but how do i illustrate derivation of the answer using fractions and equations?  hmmm... hmmm... hmmm... goodness, isn't this like love?  you just know.  cannot be.  such logic is not acceptable in class.  let's see:

50% = 50 ÷ 100
50% = (50/50) ÷ (100/50)
50% = 1 / 2

½ x n = 15
n = 15 ÷ ½
n = 15 x 2/1
n = 30

whew!

another one:

33 ⅓ % of what number is this number?

hmmm... i use a calculator for this one.  i get the answer.  but i couldn't show the derivation.  my nephew mentions something about improper fractions and cross multiplication.  waaaah!!!  ok, show tita.  i am perplexed  ->  moron-streak surfacing big-time... : }

20 items.  we were able to get the answers and show their derivation for 15.  the five, i was stumped.

my sister arrives.  my nephew tells her we are having a hard time with his homework.  she says she'll check after dinner.  ok.

later, our nephew shows her.  her reaction:  'huh?!  i thought you were solving something difficult???!'

yikes!  so the moron in me is not just a streak after all???  woe!