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Question 957892: "CONCEPT REVIEW PROBLEMS"
I don't really understand this! Could someone really, explain me what should I do when I encounter this type of problems? I get stuck every time I see this.
This is the problem: "For all real numbers a and b, let a*b=a+3b. Compare: A. (2*0)*5 B. 2*(0*5)."
Possible answers: A if "A" is greater. B if "B" is greater. C if "A" is equal to "B," and D if not sufficient information is given to figure out an answer at all.
I think I understand that "*" is only a symbol, not really the sign for multiplication. But I don't really know what to do. Help?
Thank you in advance.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! everywhere you see a*b, you replace it with a + 3b
first we work with A = (2*0)*5
2*0 is equal to 2 + 3(0) which is equal to 2.
the expression becomes 2*5.
2*5 is equal to 2 + 3(5) which is equal to 2 + 15 which is equal to 17.
A is equal to 17.
Now we work with B = 2*(0*5)
0*5 is equal to 0 + 3(5) which is equal to 15.
expression becomes 2*15.
2*15 is equal to 2 + 3(15) which is equal to 2 + 45 which is equal to 47.
B is equal to 47.
B is greater than A.
that would be selection B.
their use of * is unfortunate because * is already used to indicate multiplication which can cause great confusion if you're not aware of that.
a different symbol would have been more appropriate.
especially one that is not confused with other arithmetic symbols.
a$b would have been better because then a$b would mean a + 3*b.
this allows you to use the * the way it was originally intended to be and makes translating much clearer.
I'll do it again, but use $ this time instead of *.
A = (2$0)$5
2$0 = 2 + 3*0 = 2
expression becomes 2$5
2$5 becomes 2 + 3*5 which becomes 17.
because you are using the $ symbol rather than the * symbol, it allows you to use the * symbol the way it was intended to be used, eliminating the confusion.
B = 2$(0$5)
0$5 is equal to 0 + 3*5 which is equla to 15.
expression becomes:
2$15
2$15 is equal to 2 + 3 * 15 which is eqal to 2 + 45 which is equal to 47.
they could really blow your mind when they use the same symbol to mean two different things.
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