Monday, July 21, 2008

An answer to an anonymous challenge question

Anonymous said...
Would you like a challenge?
Alan saved $115 more than Ben. After Alan gave $17.50 to Ben, the ratio of Alan's money to Ben's money was 3 : 1. How much money did each of them save?


I think I have it figured out!

Alan saved $115 more than Ben. After Alan gave $17.50 to Ben, the ratio of Alan's money to Ben's money was 3 : 1. How much money did each of them save?

First things first, read the problem sentence by sentence underlining the who and what

Alan saved $115 more than Ben. After Alan gave $17.50 to Ben, the ratio of Alan's money to Ben's money was 3 : 1. How much money did each of them save?

Step two: List the varibles:

Alan's savings

Ben's savings

Step three: draw a unit bar to model each varible, make these all the same size
Alan's savings[][][]

Ben's savings[]

Step four: determine what each unit bar represents and where you need to place a question mark.

In this problem we need to determine how much money Ben started with, and how much Alan started with.

Alan's money [][][] + 17.50?
Ben's money []?

Step five: compute the problem
I went with what I knew:
Alan's $ to start with was = Ben's starting $ + 115
Ben's $ + 115 + 17.50 = 3:1
Alan's $= 22.50 + 115 - 17.50 = 120/4 = 30

Alan's money [30][30][30] + 17.50?
Ben's money [30]-17.50?

Alan's money to start with would have been $137.50, Ben's money to start with would have been $22.50.


I used a lot of guess and check on this problem to get the answer. I knew that I had to add
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