Wednesday, December 5, 2007

PROBLEM OF THE WEEK #14

Suppose two new mathematical operations have been invented called * and ▲.

If a * b = a + b + b and

ab = a + a – b,


How much larger is 6 * 4 than 6 ▲ 4?

19 comments:

Leslie said...

I think comparing the new signs to signs we do know will help

Anonymous said...

this'll take forever what is the answer 13 or sumtin this is like impossable

Mrs. Cooper said...

Hint...
First try to find 6 * 4 using the definition of *

Daniel Gordon said...

Maybe we should try this-
6*4= ?
a*b=a+b+b
Compare and contrast and try fitting in nmubers into these two equations.

Ethan said...

does * mean to add the second number twice plus the first one and does the triangle mean to add the first number twice and then subtract the second number

Mrs. Cooper said...

The operations of * and triangle are given. Ethan, you are on the right track!

Anonymous said...

is the * what ethan said and the ^ subtract b from a and then multiply b and the number when subtracted

Sloan Krakovsky said...

Mrs. cooper, i'm just typing this to say that i went on the blog and before i tried to figure it out i read the comments and BEN's gave away the answer so i couldn't do it but i went on

Daniel Gordon said...

i'm confused.
does * = first # + 2 # + 2 #
and ^ = first # + first # - 2 #
?

Daniel Gordon said...

That would meen that 6*4= 14 and 6^4 would= 8 which would meen that 6*4 is 6 greater than 6^4

Ethan said...

I think that Daniel is right

Ethan said...

I think that Daniel is right

Mrs. Cooper said...

Keep it up---You are all doing great

Iris said...

The difference isn't always 6. Like if a=7 and b-4, 7*4=7+4+4=15
and 7^(triangle)4=7+7-4=10. The difference here is 5, so it can't be 6. I think that the difference shouldn't be in numbers. I, also, tried a=8 and 5=b. I got a difference of 7. I think that the difference should use variables, as in the problem.

Sam said...

daniel is right you guys because a*b = a+b+b so 6*4 = 6+4+4=14 and a^b = a+a-b so 6^4 = 6+6-4=8 and 14-8=6 so 6 is the answer.

Mrs. Cooper said...

Good job! You did a great job of helping each other!
6+4+4 = 14
6+6-4 = 8
So the difference is 6.

Yacova said...

so i read what everyone said and i still dont completely understand the question. Is there anyway somebaod could rephrase it?

Mrs. Cooper said...

Yakova, See if this helps...
This operation called * is defined to be a*b = a + b + b
So let a = 6 and b = 4 and replace the a and b with the numbers. That will give you an answer for a*b.

Mrs. Cooper said...

So a*b = a + b + b means to find 6*4 use a = 6 and b = 4 and do the problem: 6 + 4 + 4

Then a triangle b = a + a - b means to find 6 triangle 4 use a = 6 and b = 4 and do the problem: 6 + 6 - 4.

so the answer is 14 - 8 = 6.