help please, i really need help on this!!?

Question

Problem # 1:
A full propane gas tank weighs 32 pounds. After 3/4 of the gas is used up, the tank and the remaining gas weighs 14 lbs. The weight of the tank when empty is_____ lbs.

Problem # 2 :

just imagine a square window, u know, with all the bars in between, to make the window look like four little squares, the regular kind of window. remove two lines only, to leave only two squares. i have tried everything, its really hard.

Problem # 3:
(imagine a circle, its a regular circle, not an oval) Draw only three lines to divide the circle in to eight(equal, i think) sections.
thank you so much!!

Answer 1

The answer to the first one is easy

if x is the weight of the gas and T is the weight of the tank, then when it is full

X+T= 32 pounds

When it 3/4 empty

.25X +T = 14 Pounds

Solve for T in equation one and put it into equation two

T=32 -X

.25X + (32-X) = 14 Pounds
18 Pounds =.75X

So X = 18/.75 Pounds

X = 24 pounds which is the weight of the gas.
Put this number back into one of the first two equations to get

T = 8 Pounds = The weight of the empty tank

#2 I'm not sure on the second one. I could make it into two rectangles, but not squares

#3 Its easy, its like a Pizza cut into 8 pieces

Answer 2

#1 Well we know that the full thank weights 32 pounds and 1/4 full (or 1/4 empty if you are the pesimistic type) weights 14 pounds. Ok so lets subtract these two numbers to see how much 3/4 weight.

32 -14 = 18

18 is how much 3/4 worth of gas weights. So if I divide that number by 3 I will get the weight of each 1/4.

18/3 = 6 pounds per quarter

so every quarter weights 6 pounds. If I multiply 6 x 4 I will get how much the gas will weight in a full tank(for that particular tank. it all depends on the tank size right). anyways,

6*4=24.

finally subtract this number from the total weight and you will be left with the weight of the tank.

32-24 = 8 pounds.

#2 geesh I can't figure this one out either because I always get left with rectangles not sqares. I guess if we consider that a rectangle is like a square then we just remove two sections and get left over with two big glass rectangles. But this is thinking that the lines that make the glass square are 4 separate ones instead of two big lines. If they are just two big ones then you can just remove those and be left with the frame. The frame is actually two squares one inside the other. This would solve the problem. The thing is I don't know what is legal or not for this problem but, is better to put something down instead of leaving it blank.

#3 I don't know. The most I can get is seven sections and they are not of equal size.


Adendum. After posting my answer I read some of the other submissions. I disagree with the solution given by mahan or was it haman for problem 3. If you cut the circle horizontally like a a cake you do get 4 sections indeed. The problem is that this aproach violates the definition of a circle. Being able to cut it horizontally like a cake implies 3 dimensions making the circle a cylinder. Just as a pyramid and a triangle are different things.

Answer 3

I'm not sure what type of mathematics you need to show to your teacher, but here's how I thought about #1:
The tank and gas weighed 32 pounds when it was 100% full. After 3/4 of the gas was used, the tank and gas weighed 14 pounds. 32 - 14 = 18 pounds for the weight of the gas used. Every 1/4 of the tank would be 6 pounds, since 18/3 is 6 where 18 is the pounds used and 3 is the number of fourths of the tank involved. Therefore, if you subtract 6 more pounds from the remaining 14, the tank would be empty of gas and weigh 8 pounds. If you draw a picture of a rectangular tank, cut it into fourths and label the top of the tank "32" and the line at the first 1/4th mark "14," it might help you see what I'm talking about. The next two lines would be "20" and "26," in order to keep the levels equal (it's a pattern of numbers), so the bottom of the tank would be "8." You have 8 pounds left to account for when the gas is gone, so that is the weight of the tank.

Answer 4

Let the weight of the tank =x
& the weight of the gas=y
so x+y=32--------------------(1)
& x+1/4 y=14
or 4x+y=56-------------------(2)
subtracting (2) from (1),we have
-3x=-24
or x=8 lbs is the weight of the tank.
2) It is not clear.
3) You can divide a circle into 8 equal parts by drawing four lines,two perpendicular to each other & two exactly making 45 degree to them,all through the center.

Answer 5

1) you need to find out how much the gas weighs. since 3/4 of the gas weighs (32 - 14)lbs, then 3/4 of the propane weighs 18 lbs. tto find out how much the gas weighs:

3/4x = 18
x = 24lbs = ttl weight of gas.

weight of full tank - weight of gas = weight of empty tank
32 - 24 = 8lbs

2)take away the full line on the far left (the left line of the big square and the top line of the bottom left little square

3) pretend its a circular prism (like a birthday cake) you can cut it in quarters, then cut it in half (like separating 2 layers of the cake)

Answer 6

1 ) empty tank weighs 8lbs

subtract the 14lbs lbs from 32lbs. Thats 18lbs. 18lbs will represent 3/4 of the tank... or 6lbs per 1/4tank. so... subtract another 6lbs for the final 1/4th of a tank and that leaves you with 8lbs for the empty tank

Answer 7

1) set up 2 equations :let x be weight of gas
let y be weight of tank

x+y=32
1/4x+y=14 Use elimination to get rid of y and solve for x. Then substitue back into x+y=32 and get value of y.

Answer 8

Less time on Yahoo and more time studying your homework is the real answer.

Problem 2: Remove the vertical bars.

Answer 9

Problem #1: Answer is 8 lbs
Problem #2:
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~ there's that small one and the whole window~
Problem #3: Are the lines straight?