
Re: Simplifying Algebraic Expressions with Subtracted Expressions
Posted:
Nov 14, 2013 1:44 PM


On Nov 14, 2013, at 12:51 PM, Joe Niederberger <niederberger@comcast.net> wrote:
> Lou Talman says: >> Here is one such problem, as given by Ma: "Mrs. Chen made > some tarts. She sold 3/5 of them in the morning and 1/4 of the remainder in the afternoon. If she sold 200 more tarts in the morning than in the afternoon, how many tarts did she make?" > > LiPing Ma goes on to illustrate the "solution" as a working out of this "starting point" arithmetic expression: 200 % (3/5  1/4(13/5)). > > What is the thought process that guides the formation of such an expression? Or, what is an English translation of that expression that relates naturally to the word problem as given? Is there any way to do so without mentioning the implicit "x"? > > Cheers, > Joe N
I thought that at first as well, but when you look at the problem a bit (and forget your algebra training) you can see how it is decoded in one pass (without an implicit x). Look at this problem...
Sam and John were paid 21 dollars total and Sam was paid twice as much as John, how much were each paid?
We tend to look at this as S + J = 21 and S = 2J, but you can literally (without some implicit x) see this as John and 2 Johns equal 21 and thus John = 7.
The Ma problem works the same way, through literal substitution...
3/5 {morning batch)
minus
1/4(13/5) {evening batch} < This is the literal interpretation of what was written.
equal
200
Bob Hansen

