Word problem havok, can anyone help?

Question

Wally has 100oz of celery that is 99% water. After sitting in bright sunlight, the celery dried out and became 98% water. How many oz does the celery now weigh?

Hint: The celery will weigh much less than 90 oz.

Answer 1

before drying
99 oz. water + 1 oz. not water = 100 oz. wet celery

after drying
98 X water + 2 X not water = 100 x dry celery
substitute 2 X = 1 oz (The not water part stays the same), X = 0.5 oz
98 (0.5 oz) water + 2 (0.5 oz) not water = 100 (0.5 oz) dry celery
49 oz water + 1 oz not water = 50 oz dry celery

The dried celery weighs 50 oz.

Answer 2

There is a straightforward equation for finding the new weight of the celery.

If the celery weighed 100 oz. and it loses x oz., then its new weight is (100 - x) oz. Likewise, if the celery originally contained 99 oz. of water and lost x oz., then the weight of the water is now (99 - x) oz. Now all we have to do is figure out how to relate these two figures.

Since the new weight of the water, (99 - x) oz., now represents 98% of the entire new weight, (100 - x) oz., then we can relate them this way:

(new weight water) = 0.98 (new weight celery), which is equivalent to this:

(new weight water) / (new weight celery) = 0.98

Substituting in the values we assigned earlier, we get this final form for our equation:

(99 - x) / (100 - x) = 0.98

Convert the above equation to its linear form to find x:

(99 - x) = 0.98 (100 - x)
99 - x = 98 - 0.98 x
-0.02 x = -1
x = -1 / -0.02
x = 50

So, the celery lost 50 oz., which means it now weighs (100 - 50) = 50 oz. and there are now (99 - 50) = 49 oz. of water in the celery.

Now, to check to see whether our calculation is correct, divide 49 by 50. If it is, then the decimal number which results will be 0.98. In this case it is. So 50 oz. is the correct answer.

Answer 3

Initilally the celery consisted of 99oz of water:

99% of W(weight) = W x 0.99
= 100oz x 0.99
= 99oz

and 1oz of "solid matter":

100% - 99% = 1%
100oz * 0.01 = 1oz

After drying, there was less water, but the amount of "solid matter" would have stayed the same. Since we know that the ratio of water to solid matter after drying was 98 to 2:

100% - 98% = 2%

the question really is
"If 1oz is 2% of a total mass, what is the total mass (or 100% of the total mass)?":

2% goes into 100% 50 times:

100% / 2% = 50

so the total mass must be 50 times 1oz:

50 x 1oz = 50oz

And that is the answer. After drying in the sun, the celery weighed 50 oz.

Answer 4

originally: water = .99% (100 oz celery) = 99 oz of water

celery substance = 100 oz - 99 oz water = 1 oz


say L = water lost after drying, then

99 - L = amount of water left
100 - L = amount of celery left

the amount of water left is 98% of the amount of celery left

99 - L = .98 (100 - L) [solve for L ]

99 - L = 98 - .98L

1 = .02 L

L = 1/.02 = 50 oz of water

The water remaining is 99 oz - 50 oz = 49 oz
The celery substance remains constant = 1 oz

Therefore after drying the celery weighs 49 + 1 = 50 oz.

Answer 5

If the celery is 100 oz and 99% of it is water, then it must have 99 oz of water and 1 oz of actual solid celery. Then it loses some amount of this water until the amount of water left is 98% of the celery. If this lost amount of water in ounces is w, then

remaining water = 98% of (remaining water plus solid celery)
(99-w) = 0.98( (99-w) + 1)
99-w = 0.98*99 - 0.98w + 0.98
99 = 0.98*99 + 0.02w + 0.98
98.02 - 0.98*99 = 0.02 w
1 = 0.02w
w = 50 ounces

So if 50 ounces of water evaporated, then there must be 99-50=49 ounces of water left, and still the 1 ounce of dried celery. So the total weight is now 50 oz.

Answer 6

In the beginning, the celery has 1 oz "solid" and 99 oz water
After it stayed in the sun, some water went away, and now it has x oz water, however, the solid remain the same, 1 oz

x = .98 (1+x) -> .02x = .98 -> x = 49 Oz
So, total is 49+1 = Celery weights 50 Oz

Answer 7

99% water + 1% celery = 100 oz.
water=99oz. actual celery=1 oz.
vs. water 98% actual celery 2%

If it were 100% water at 100 oz. and we loose 1% of the water - the water remaining will weigh 99 oz.

'Tain't very likely the 1 or 2% of celery will make the difference you indicate in your hint. Are you looking for the actual DRY weight of the celery?

Answer 8

The "celery weight" is 100 oz 8 (1- .99) = 1 oz
When the celery dries out to 98% water
W = 1/0.02 = 50 oz

Answer 9

celery = water + solids (non-water)

C = W + S
C =100
W / C = 0.99 => W = 99, S = 1
After drying, W' is the new amount of water, and C' is the new weight of the celery. The amountof water lost is L = W - W'
C' = W' + S
W' / C' = 0.98
W' = 0.98 * C'
W - L = 0.98 * (C - L)
99 - L = 0.98 * (100 - L)
99 - L = 98 - 0.98L
1 = 0.02 L, L = 50
C' = 100 - 50 = 50