Originally Posted by Bill Verburg (Post 8727162)

This type of question has been commonly showing up on HS Introductory algebra tests for decades

the # and * are abstract operations which are defined in the statement of the problem, other symbols, &,%,? etc. are commonly used as well, * is not multiplication this is mistake one.

The object of the question is to determine if the student can follow the abstract rules as presented w/o having any prior experience w/ them and then evaluate the resulting expression using the common math operations.

a * b = a - 3b is the definition of the * binary operator in terms of the usual subtraction binary operator and implicit binary multiplication using the variable values of a & b

similarly a # b = 2a+3b is the definition of the # binary operator in terms of the usual addition and implicit multiplication binary operators using the variable values of a & b.

the substitution principle, use of parenthesis and the use of the unary - operator are also involved in the solution.

starting w/ a=4, b =5 because it is inside parenthesis
a * b = a - 3b
becomes
4 * 3
4 - 3(3) per the def of * and substituting
4 - 9 regular arithmetic
-5

and then using the def of #
a # b = 2a+3b
(4 * 3) # 5 note that the current value of a was derived in the previous step as -5
(-5) # 5 implicit multiplication by 1 implies 1(-5) = -5
-5 # 5 the current value of a is -5 and the current value of b is 5
2(-5) +3(5) per the def of #
-10 + 15
5

Originally Posted by bell (Post 8727332)

42

Originally Posted by Flieger (Post 8726894)

Please Excuse My Dear Aunt Sally. ;)
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Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.

Originally Posted by Bill Verburg (Post 8727162)

..., * is not multiplication...

Originally Posted by Bill Verburg (Post 8727162)

This type of question has been commonly showing up on HS Introductory algebra tests for decades

the # and * are abstract operations which are defined in the statement of the problem, other symbols, &,%,? etc. are commonly used as well, * is not multiplication this is mistake one.

Originally Posted by wdfifteen (Post 8727918)

If by mistake you mean mistake in the presentation of the problem, I agree.
If commonly accepted symbols for operations are arbitrarily redefined, the all of the commonly accepted symbols for operations are open to redefinition. Under these circumstances, why assume ( x+xx ) means three numbers and an addition operation are inside brackets? Why assume there is a set of brackets at all? The left bracket could have one meaning the +could have another meaning, and the end bracket could have yet another meaning. I understand this as an exercise in logic and deduction, but mixing redefined common symbols for operators with arbitrary meanings for operators is just chaos.

Originally Posted by Bill Verburg (Post 8728072)

.wiki has a fair summary of what is correct, some will be familiar to you others will not

when these problems are presented the symbols are generally chosen to avoid vernacular confusion, often using Greek or other non ambiguous symbols

no this isn't convoluted or confused, just something most of you aren't familiar w/..

Originally Posted by island911 (Post 8728121)

Are you sure?

Or did you just not -get- the convolution reference?

http://forums.pelicanparts.com/uploa...1438026212.jpg

;) get it now.. confused convolution used in a thread about avoiding vernacular confusion about *

https://en.wikipedia.org/wiki/List_of_mathematical_symbols#Other_non-letter_symbols

I maintain, this was a poor choice of operational variable.

Originally Posted by island911 (Post 8726777)

+1 to Flieger (never seen anything like that)

fwiw, I've always maintained that the problem with math is that it is usually taught by math majors. --they get in to useless math games. I would hate math if it were not for engineering teachers demonstrating the power of math in application. (a tool)

To put it another way, math is but a language for representing quantifiable relationships. Essentially, equations are sentences, with math syntax, which model relations. Math geeks, however, get into the structure of the syntax and completely lose sight of application. Thus, they create ridiculously useless syntax puzzles like above.