Math Question Help Needed
 

My son has a problem in his math book that has not shown itself in previous lessons and I was hoping someone here could help.

If a * b = a - 3b and a # b = 2a+3b, evaluate the expression (4 *3) # 5.

In a problem like this, what does # mean? He has several of these types of problems in the next few lessons and I want to make sure we understand it fully. I have looked in my teacher's book and it has a poor explanation.

TIA

" it has a poor explanation"

there ya go.

It's not you (or kid) it's the teacher not defining the language. (symbols)

It's not for a programming class, right?

I homeschool so I am the teacher.

If it helps, this is a trig/pre-calculus book.

Ha!

Okay, let's learn about typo's ! :D

If not, let's see the explanation.

so.. # is the symbol for an unknown math operator? As in, solve for #(unknown math operator) ?

yeah ...

Why doesn't the problem ask it that way? (I know, math geeks are weird)

The solution:

We are given that a * b= a - 3b. To evaluate 4*3, we must recognize that a corresponds to 4 and b corresponds to 3.

If a*b=a-3b, 4*3=4-3(3)=-5
Since 4*3=-5, (4*3) #5 = -5#5

To evaluate -5#5, we see that a#b=2a+3b, and recognize that, in this case, a corresponds to -5 and b corresponds to 5.

If a#b = 2a+3b, -5#5 = 2(-5)+3(5)=5
So, (4*3)#5=5

I believe the answer is 2(4-3(3))+3(5)=5

Seems more like a logic puzzle than a math question, though. I can tell you I have an engineering degree and never came across this question.

Dang, you beat me to it. :)

+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.

Thanks for all the help. Please excuse any dumb questions, it is still a little above me.

In the explanation I put up, the first line reads:

If a*b=a-3b, 4*3=4-3(3)=-5

Where does the -5 come from?

Nevermind. Working through it again and it just clicked. Sometimes my brain does not move as fast as I want it.

Thanks for all your help.

My daugher is only 11 and her math already makes me think on occasion. I am so doomed.

I know. Next year he will take Calculus at the local university and he will only be 16.

Ultimately with this problem, I overcomplicated things in my head. It really is a simple substitution problem but I was thinking it must be something more because of the level of math book. That will teach me to think too much. ;)

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

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

42

I guess I don't love maths.

42