I saw a post on another blog (check the entry for December 29th) asking for help on a math problem. As a “regular” math problem, it is fairly straight forward and easy to solve. However, Singapore throws a curve into it by asking for it to be solved using a bar graph. Here’s the story problem:
“Albert had $16.10 less than Peter. After Peter gave $2.50 to Albert, he had 4 times as much money as Albert. How much money did Peter have at first?”
First, the algebraic way to set it up, just to get it out of my system. One sets up two simultaneous equations where A is the amount Albert had at first and P is how much Peter had at the beginning. One then solves for P.
A = P – $16.10
(P-$2.50) = 4*(A+$2.5)
But, as I said, Singapore wants this solved using a bar graph. That gets a bit trickier, but I’m assuming since Singapore also likes mental math that my solution is somewhat acceptable. Let me lay it out.
To rephrase the problem, Peter has $16.10 more than Al. That’s my first bar on my graph. Then, Peter gives $2.50 of his money to Al and the resulting amount that Peter has is four times how much Al has. So, Peter has four times Al’s original amount plus four times $2.50 plus another $2.50 that he subtracted from his amount.
When drawn graphically, one realizes quickly that if one cuts the original “P” bar down by an “A,” it is equal to the $16.10 from the original problem. Here are my two (not to scale) bars:
That leaves just some mental math to finish out the problem. 5*2.5 = 12.5 (as indicated on the side of the graph). $16.10 – $12.5 = $3.6 = three times Al’s original amount. Al’s amount is $1.20. That makes Peter’s original amount $17.30.
A double check of the solution of the simultaneous equation solution from above reveals the same amounts.
Do I know my solution is the one Singapore is looking for? No.
Does it get one there? Yes.