Two problems that are giving me hell

Question

Problem #1.

A rectangular tabletop consists if a piece of laminated wood bordered by a thin metal strip along its four edges. The surface area of the tabletop is x square feet, and the total length of the strip before it was attached was x feet. If the tabletop is 3 feet wide, what is its approximate length, in feet?

(A) 12
(B) 10
(C) 9
(D) 8
(E) 6

Answer is E

I have no idea what they are asking.

Problem #2.

For all real numbers v, the operation v* is defined by the equation v*=v-v/3. If (v*)*=8, then v=

(A) 15
(B) 18
(C) 21
(D) 24
(E) 27

Answer is B

Thanks a bunch.

dmateer25 · Answer

Here is how i solved problem 2

You know the operation is v* is defined by v – v/3

So plug in your answer choices into this first. Then the answer you get from this needs to be plugged back in a second time.

Starting with A:

A) 15 – 15/3 = 15 – 5 = 10 now plugging in a 2nd time we get 10 – 10/3 and this doesn’t equal 8.

b) 18 – 18/3 = 18 – 6 = 12 now plugging in a 2nd time we get 12 – 12/3 = 12 – 4 = 8.

Bingo, B is the answer.

480ocean · Answer

Dmateer225, I'm having a hard time reconciling this in my mind. How would we know to plug the first answer (12) into the equation again?

awesomeusername · Answer

Here is my stab at #1:

So here is what we know:
1. The area of the tabletop is x square feet.
2. The width of the tabletop is 3 feet.
3. The length of the metal trim is x feet

The question is asking for the length of the tabletop. We have two equations:

Area = length times width
So we then have x = L x 3

The perimeter of the tabletop is:
P = 2L + 2W
So we know that the metal trim around the perimeter of the tabletop is x.
Thus,
x = 2L + 6

Now we have a system of two equations:
x = L x 3
x = 2L + 6

3L = 2L + 6
L = 6

(E)

yasik19 · Answer

dmateer25 wrote:Here is how i solved problem 2

You know the operation is v* is defined by v – v/3

So plug in your answer choices into this first. Then the answer you get from this needs to be plugged back in a second time.

Starting with A:

A) 15 – 15/3 = 15 – 5 = 10 now plugging in a 2nd time we get 10 – 10/3 and this doesn’t equal 8.

b) 18 – 18/3 = 18 – 6 = 12 now plugging in a 2nd time we get 12 – 12/3 = 12 – 4 = 8.

Bingo, B is the answer.

Thanks. But isn't the answer supposed to be something to the power of that same thing?

awesomeusername · Answer

We know v*=v-v/3. Then (v*)* =

((v-(v/3)) - ((v-(v/3))/3 =
* Above is because we replace v-v/3 where we see a v in (v-v/3)

((3v - v)/3) - ((3v - v)/9) =

(2v/3) - (2v/9) =

((6v - 2v)/9) =

4v/9

Thus 4v/9 = 8

v = 72/4 = 18

It appears that the above explanation of plugging and playing will be the simpler way to go if you're not comfortable with algebra. I'm just showing you that there are no squared variables involved.

chykie · Answer

my stab @2

(v*)* = 8

let's work the outer first
substitute v* = u
so (U)*= 8

u-u/3 = 8
(3u-u)/3 = 8
3u-u= 24
2u= 24
u= 12

Let's put back the U
so
u= 12
then (v-v/3)= 12
(3v-v)/3= 12
3v-v=36
2v=36
v=18

Hope it helps.

yasik19 · Answer

thank you both so much, I just now realized that i'm a moron.

gaggleofgirls · Answer

In Problem one, they have told you the area of the table top as XsqFt and the perimiter of the table being the length of the edging before it was applied as X and the width as #.

So, the Area = Width * Length= 3L
The Perimeter = 2(Width) + 2(Length) = 2*3 + 2L = 6 + 2L

Since both the area and the Perimeter = X units, then they equal each other, so

3L = 2L + 6
L=6

Answer is E

-Carrie

chintudave · Answer

I would stick with awesomeusername's method for the 1 problem.

Here is my stab at the second one...

V* = V-V/3

i.e. V* is nothing but two third V... 2V/3
Extending the above ... (V*)* = 4V/9

Given 4V/9 = 8, so V = 18

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