A Jelly Problem

The answer is that the jelly would now weigh 50 pounds!

When the jelly weighs 100 pounds, it is 99% water. That means that it is 1% non-water, and this non-water component of the jelly must weigh one pound.

After evaporation, the non-water component accounts for 2% of the weight of the jelly. So 2% of the jelly weighs one pound. Scaling this up, we see that, if 2% weighs one pound, then the entire jelly must weigh fifty pounds.

let consider new weight is X

X= 1 (solid) + 98%(X)

X=1+0.98 X

X=50

Let the decrease in water weight be $x$ . Since percentage of water weight was 99%, it weighs 99 pounds. A 1 pound decrease in water weight would correspond to a 1 pound decrease in overall weight. From provided information: $\frac { 99-x }{ 100-x }=0.98$ . Solving the equation yields $x=50$ . Therefore, total weight now is $100-50=50$ pounds.

There is one thing I'd like to clarify in this problem. It shouldn't just be the water evaporating, because that's not the same thing as the mass being decreased. Anyways, the way to solve is by setting up the following proportion, where $x$ is the amount being taken away:

$\frac{99-x}{100-x}=\frac{49}{50}$

Cross multiplying and rearranging produces

$4950=4900+x$

Solving, $x=50$ . Thus the amount of jelly left is $\boxed{50}$ .

nice problem

The initial ratio of water : jelly is 99 : 1

now let x be the weight of the water that dries up.

The new ratio is (99-x)/1 = 98/2

solving this, x = 50

so new weight of water is 99-50 = 49

and the weight of jelly remains 1

so, total weight is 49+1 = 50

The equation created will be ( (99 - x)/ (100 - x) ) x 100= 98 . Since water and weight will decrease by the same amount because water is evaporating. The equation is solved by 9900 - 100x = 9800 - 98x. Hence 100 = 2x and x = 50. Please note that x is the amount of water lost. So weight of jelly equals 50 pounds and weight of water equals 49 pounds.

This one is similar to the discussion a week back, taking potatoes in place of jelly, it took me reading twice to understand it and it is cool. 99% goes to 98%, leaving 1% weight (1 pound initially) to 2% (that is still 1 pound). total is 100%, and 1 pound equals 2% so 100/2 = 50 lbs.

the following tabulation works: nw is nonwater, w is water all weight being in pounds (nw, w, jelly) = (1, 99, 100) before and =(1, x, 1+x) after; since after, it is 98% water by weight, one has (1+x)/x = 100/98 whereby x=49 and jelly weighs 1+x = 50 pounds.

Initially, the jelly had 99% water or we may say 1% of other substances.. i.e., 1pound.. Later when some of the water evaporated, mass of the other substances would still have been 1 pound only.. now this time water constitutes 98% of the total mass , therefore, the other substances made 2% of new mass (say x) i.e., 2% of x = 1 pound 2/100 * x = 1 pound x = 50 pound

as it is given 99% water i.e. 99 pounds of water and 1 % jelly substance i.e. 1 pound jelly substance.

now,

let x be the about evaporated, therefore, amount of water left = 99-x and total amount of jelly = 100-x then

99-x/100-x = 98 ............(given)

solving it we get x=50 total weight of jelly left = 100-50 = 50 pounds

The weight of the gelatin is 1 pound (1% of 100). If the water percentage goes down to 98%, it is now 49/50 of the jelly. The rest (1/50) is gelatin, and it weighs 1 pound, so 50/50 must weigh 50 pounds.

Let x be the quantity of water after reduction. then: x/(1+x)=98% where 1 represents the dehydrated weight of jelly.(1-99% * 100pt.) Solving we get x = 49, so, Water contend + Dehydrated weight of jelly = 49 + 1 = 50pt.

Initially in 100 pound jelly there was 99%water i.e. 1 pound solid. Now let weight of water be 'x' pound x/1+x = 98% 2x =98 x=49 1(wt. of solid)+x( wt. of water) =50pound

The weight of Jelly = Weight of Water + Weight of Solid. let J = weight of jelly let W = weight of water let S = weight of solid since J = 100 and it is 99% water by weight, then W = 99, and S = 1. since weight of solid is constant, the formula for %mass of water is W/W+1 solve for W in the equation (W/W+1) = 0.98, you get W = 49. since J = W+S, then J = 49 + 1 = 50

jelly has 99 parts water and 1 parts mass. mass will remain constant i.e will not be altered after evaporation. so, x being new parts of water.

X/(X+1)=0.98 X=49. Hence,New weight = 50.

Among 100 pounds 99% is water.so water =99 pounds and non-water=1 pound.After evaporating non-water will remain 1 pound.Let, the jelly now weighs X pound,so 98%X+1=X.solving above equation X=50

Since the Jelly is $99 \%$ water by weight, the remaining $1 \%$ , that is $\dfrac{1}{100} \times 100 = 1$ $\text{pound}$ is stuff that cannot be evaporated. That will remain constant.

After evaporation, let the content of Jelly by $x$ . Now, the Jelly is $98 \%$ water by weight.

Hence,

$\Rightarrow \dfrac{98}{100}x + 1 = x$

Solving this, we get $\boxed{x = 50}$ .

2% of the weight is made up of solids, we know from the first section that the solids weigh 1 pound, so if 2% of the weight is 1 pound, 100% of the weight is 50 pounds

The amount of Solid is going to remain same before and after because it is not evaporating . so , it is 1% by weight before i.e. 1 Pound and at last it becomes 2% by weight i.e. now 2% is equal to 1 pound . Hence , weight now becomes 50 Pounds .

let x = pound lost

since 99% of 100 = 99, the initial amount of water must be 99 pounds, and the remaining 1 lbs must be the other content. since we are looking for the amount of water evaporated, 99-x = .98(100-x) ; x = 50 ; 100 - 50 = 50

The key to the answer is that the weight of the non-water part of the jelly will remain constant.

Initially, 99% is water. So within 100 pounds, 99 pounds are water, 1 pound is non-water.

Next, after evaporation, let the weight of the jelly be x.

So, 0.98x = water and 0.02x = non-water

As weight of water and non-water part is constant,

0.02x = 1 x = 50

So, weight of jelly after evaporation of water = 50 pounds.