Honey Bottle

1500 - 900 = 600 (half honey)

600 (half honey) + 600 (half honey) = 1200 (honey)

1500 - 1200 = 300 (bottle)

Let the bottle weight be $x$ and let the honey weight be $y$ .

The weight of the bottle with honey is 1500g,
Therefore $x + y = 1500$ grams _ _ _ _ _ _ _ _ (1)

Then the weight of the bottle with half of the honey is 900 grams,
Therefore $x + \dfrac y2= 900$ grams
That is $2x + y = 1800$ _ _ _ _ _ _ _ _ _ _ _ __ (2) ,

Solving the first and second equation , $2x + y = 1800 , x + y = 1500$ , we get
x = 300

Therefore the weight of the bottle is 300 grams.

When Bottle is full of honey it weighs 1.5 kg = 1500 grams

When it is half of honey it weighs 900 grams

It means half a bottle honey weighs 1500-900 = 600 grams

So full bottle honey weighs (excluding bottle weighs) = 600 +600= 1200 grams

1500 -1200 = 300 grams is the answer :-)

2 half filled bottles of honey weigh 1.8kg together. If 1 full bottle of honey weigh 1.5 kg, the bottle weighs 300 grams.

2(900)=1800, 1800-1500=300

Let the bottle's wight be represented by x , and the honey's weight (amount that fills bottle) represented by y .

Since the weight of the bottle filled with honey is 1500 grams, we can say:

x+y=1500

Since the bottle of honey half empty weighs 900 grams, we can say:

x+ $\frac{y}{2}$ =900

Using system of equations, we can use these two equations to find the value of x and y. We can use substitution:

x+ $\frac{y}{2}$ =900

x=900- $\frac{y}{2}$

So let's input this new value of x into the other equation:

x+y=1500

900- $\frac{y}{2}$ +y=1500

- $\frac{y}{2}$ +y=1500-900

- $\frac{y}{2}$ +y=600

-y+2y=1200

y=1200

So now we know that the honey's weight was 1200 grams. But we want the weight of the bottle alone, so let's input this exact value of y into the first equation:

x+y=1500

x+1200=1500

x=1500-1200

x=300

As you can see, the weight of the empty bottle in is 300 grams.

Weight of honey + the complete bottle = 1500 g.

Weight of half honey + the complete bottle = 900 g.

Now, the weight of the complete bottle remains constant.

Reduction in amount of honey, that is , half the amount of honey = 1500 g - 900 g = 600 g.

Presently, the complete bottle contains half the amount of honey and the rest

of the weight is of the bottle.

Therefore, the weight of the bottle = 900 g - 600 g = 300 g.

Answer: 300 g

Let the weight of the bottle be x.

Since the given weight (1.5 kg and 900 g) still include the weight of the bottle, Actual weight of full honey = 1500 - x Actual weight of half honey = 900 - x

Since 900 - x is only half of 1500 - x,

1500 - x = 2(900-x) 1500 - x = 1800 - 2x x = 300

Thus, the weight of the bottle is 300 grams.

Everyone has what seems to be a more complex method than what I used to get my answer. They say full it weighs 1500g and half full it weighs 900g. So I took 1500g÷2(to find the half full value with jar weight included)= 750g. Since they say the weight is 900g half full and we know we can't take half the jar away, 900g-750g=150g. Since 150g would only be half the weight of the jar, I multiplied it by two 150g×2=300g for my answer. I don't see an issue with this method, does anyone else?

The total weight is 1500 The weight of jar +weight of half honey is 900 So the remaining weight is weight of half honey (excluding weight of bottle) =1500-900=600

1500-900=600 (weight of honey)

900-600=300 (weight of bottle)

1500 - 900 = 600

900 - 600 = 300

(I learned this in the Algebra Fundamentals course on Brilliant.)

Let the weights of the empty bottle and one bottle of honey be $W_b$ grams and $W_h$ grams respectively, we get:

$\begin{cases} { W }_{ b }+{ W }_{ h }=1500 \\ { W }_{ b }+{ \frac { 1 }{ 2 } }W_{ h }=900 \end{cases}$

From the second equation:

$\begin{aligned} { W }_{ b }+{ \frac { 1 }{ 2 } }W_{ h } & = & 900 \\ { \frac { 1 }{ 2 } }W_{ h } & = & 900-{ W }_{ b } \\ W_{ h } & = & 1800-2{ W }_{ b } \end{aligned}$

By backsubstituding into the first equation, we get:

$\begin{aligned} { W }_{ b }+(1800-2{ W }_{ b }) & = & 1500 \\ 1800-{ W }_{ b } & = & 1500 \\ { W }_{ b } & = & \boxed { 300 } \end{aligned}$

$\therefore$ The weight of the empty bottle is 300 grams.

Note: weights are not measured in grams but masses are.

$\frac{1}{2}h = 1500 - 900 = 600$ $\text{bottle} \rightarrow 900 - 600 = 300$

Picture

$1500-900=600$ (half honey)

$900-600=\boxed{\large{300}}$ (empty jar)

The first bottle is fully packed with honey, with no air left to spare. So, only honey is 1500. So, we can write; 1500 grams (Honey) ---> 0 grams (Air)

When we take half away, we are left with 750 grams of honey, but with some air. Because we know that there is some air, we can find how much by subtracting 750 from 700. This leaves us with 150 "grams" of air; 750 grams (Honey) --> 150 grams (Air)

Finally, the situation, "What is the weight of the empty bottle in grams" can be written like; 0 grams (Honey) --> ?

We can see from our previous patterns that when we subtract half of the honey, 150 "grams" of air is added. When we again subtract 750 grams of honey from 750 grams of honey, we are left with 0 grams of honey. This time, we add 150 grams to 150 grams again. 150 plus 150 is 300. So, we can write this as; 0 grams (Honey) --> 300 (Air)

Hence, the answer is 300.

(This is how I solved it, but the real weight is from the bottle.)

[[start-example]] As bottle mass with honey = 1500 g half of the honey weighs = 900 g if half of the honey weighs is 900 g the remaining part must be of 900 g so Total bottle weighs fill with honey = 900 + 900 = 1800 g 1800 g - 1500 g = 300 g Mass of empty bottle = 300 g [[end-example]]

(b)ottle + (h)oney = 1500

b = 1500 - h

Also

b + 1/2h = 900

b = 900 - 1/2h

SO

b = b

1500 - h = 900 - 1/2h

600 = h - 1/2h

600 = 1/2h

1200 = h

so

b + 1200 = 1500

b = 300

H= honey x= jar

2h + x = 1500 ---- equation 1

h + x = 900 ---- equation 2

equation 1 - equation 2

h = 600

Therefore

600 + x = 900

Therefore

x = 300

x = the jar = 300

B+H=1500 and 1/2H+B=900 solving for B gives B=300

B+h=1500,b+h/2=600 solve to give b=300

1500 is the weight of the honey and the bottle together, 900 is the honey and bottle together. 900+900=1800 1800-1500=300

900 +900 =1800 1800-1500=300 the weight of the jar which is constant regardless of the honey. so half a jar is 900-300=600 the true weight of only the honey 600+600+300 =1500

1500-900=600 such is how much weight was lost to get top half, honey

900-600 (the weight lost when losing the first half of the h honey) =300

1500-900=600, how much more honey is in the jar. 900-600 how much the jar weighs

900 x 2 =1800 1800-1500 = 300

y : weight of empty jar; x : weight of half honey in a jar;

(1). y + 2x = 1500; (2). y + x = 900;

(1) - (2). : y + 2x - y - x = 1500 - 900 = 600; x = 600; y = 900 - 600 = 300

900x2=1800. 1800-1500=300 Is less volume of honey in the half bottle but the weight of the bottles is the same. So start with 900x2=1800. 1800-1500(total weight)=300

Glass + 2 Honey = 1500 Glass + Honey = 900 So, Honey = 600 (1500 - 900)

So, Glass = 300

1500 ÷ 2 = 750 then 900 ÷ 2 = 450 then 750 - 450 = 300 So the empty bottle is 300 grams.

Half the honey bottle should be 1500/2=750, So get the half bottle with honey 900 and do 900-750=150 so the half bottle is 150 grams so to find the full bottle you do 150x2=300 since 150 is half the bottles weight without honey so twice that is the full bottle without honey 300 grams

1500 - 900 = 600 (half honey)

600 (half honey) + 600 (half honey) = 1200 (honey)

so,1500 - 1200 = 300 (bottle) therefore weight of the bottle =300g

Very easy as you know the fact that bottle weight is remain constant so taking Y as the weight of bottle X the weight of honey 1 equ wiil be Y= 1500-X Then as mentioned honey remained 1/2 so making 2 equ 1/2Y=900-X So 1/2(1500-X)=900-X Solving these X=300

1500-900= half the weight of honey Multiply that weight by 2 since we need a full amount. Reduce 1500 by 1200 which is you reducing the weight of honey from the full honey bottle to get the empty bottle. You get 300 left which is the correct answer.

Practical. And its my solutions 900 x 2 = 1800 And than substract it with its full weight 1800 - 1500 = 300

Full bottle with honey = 1500 Half bottle = 900 Empty bottle = 1500-900 = 300

900+900=1800 1800-1500=300

Constants: Honey = H Bottle = B

Equations: 1) B + H = 1500 2) H/2 + B = 900

Derivation of H: Equations, 1) - 2) = 1500 - 900 => H/2 = 1500 - 900 => H = 2(1500 - 900) H = 1200

Derivation of B: Rearranging equation 1) and substituting H B = 1500 - H B = 1500 - 1200 B = 300

Answer: Bottle weighs 300g.

By taking 900 grams away from 1500 grams this then leaves you with the weight of half the honey. Then if you do 900-600 gives you how much the bottle weighs.

Let empty bottle be x and honey be y form two eq and solve them by substraction u will get ur answer

Full bottle of honey with the bottle weighs 1500 grams and half a bottle of honey with the bottle weighs 900 grams. Hence, half a bottle of honey WITHOUT the bottle weighs 1500 - 900 = 600 grams and so the bottle weighs 900 - 600 = 300 grams.

Or simply do 900x2=1800 And then 1800-1500=300

Y+x=1500 Y+1/2x=900 1/2x=600 X=1200 1500-1200=300=y

1500/2=750

900-750=150=half the bottle weight

150*2=300=the whole bottle weight

我们可以知道半瓶蜂蜜重1500-900＝600.瓶子重900-600＝300

1500 - 900 = 600, 900 - 600 = 300 300 is the answer

Let x represent grams of total honey. Let y represent grams from jar. x+y=1500 g x/2+y=900 g Solve system of equations by subtracting equations. x/2=600 g x=1200 g Plug x in to solve for y. (1200 g)+y=1500 g y=300 g The mass of the jar is 300 g.

The bottle weight with honey is 1500

We take out half of the honey 900

So (honey & bottle) - (half honey & bottle) = (half honey)

1500 - 900 = 600

Half honey = 600

2 (Half honey) = Complete honey

2 (600) = 1200

Bottle & Honey - Honey = Bottle

1500 - 1200 = 300

If x=honey and y=jar,

2x+y=1500 and x+y=900

Therefore x=900-y

If you sub that into the first equation,

2 (900-y)+y=1500

Multiply out the brackets and you get

1800-2y+y=1500

1800-y=1500

300-y=0

y=300

Therefore the jar = 300g