Problem Solving
▪ Question:
Andrew has some magic cards to trade. Ian has 2 more than 2 times the number
of magic cards Andrew has. Patrick has 2 less than Ian. Ken has 4 less than 2 times the
number of magic cards Patrick has. Patrick has 8 magic cards. How many magic cards
does Andrew have to trade?
▪ Polya’s Four-Step Problem Solving Strategy
1. Understand the problem.
We are looking the total number of cards Andrew (x) must have to trade. Given
that Ian has 2 more than 2 times the number of cards of Andrew (2x+2). Then, Patrick
has 2 less than the numbers of card of Ian ([2x+2] – 2), or simplify to be 2x. While Ken
has 4 less than 2 times the number of cards of Patrick (2[2x] – 4). If Patrick has 8 cards,
how many cards does Andrew have. Let x be the number of Andrew’s magic cards.
2. Devise a plan.
Given:
Let x be the total number of magic cards Andrew's have
Ian= 2x+2
Patrick= (2x+2) – 2= 2x
Ken= 2(2x) – 4
If Patrick has 8 magic cards, we can use this in the formula since number of Patrick's
cards is 2 times the number (2x). Let’s use this formula, 2x = 8, to get the total number of
magic cards of Andrew.
