A certain electrolyte solution contains 1 gram of salt for every 8 gra

Question

A certain electrolyte solution contains 1 gram of salt for every 8 grams of sugar and every 200 grams of water. If the sugar to water ratio is halved, the salt to sugar ratio is tripled, and the resulting solution contains 5 grams of salt, how many grams of water does the resulting solution contain?

A. 250
B. 400
C. 666 2/3
D. 1,000
E. 2,000

A. 250
B. 400
C. 666 2/3
D. 1,000
E. 2,000

ScottTargetTestPrep · Accepted Answer

We have an initial ratio of:

Salt: sugar : water = 1 : 8 : 200

Since the sugar to water ratio is halved, we have:

sugar/water = 1/2 x 8/200 = 8/400

Since the salt to sugar ratio is tripled, we have:

salt/sugar = 3 x 1/8 = 3/8

Thus, the new ratio is:

Salt: sugar : water = 3 : 8 : 400 or 3x : 8x : 400x

Since there is 5 grams of salt:

3x = 5

x = 5/3

The amount of water is 400 * 5/3 = 2,000/3 = 666 2/3.

Answer: C

Lampard42 · Answer

Salt:8Sugar:200Water; Revised ratio of Sugar to water is 1:50 and Salt to Sugar is 3:8; 5 grams of salt will give 5*8/3=40/3 sugar which will give 40/3*50=666 2/3 water IMO C

Archit3110 · Answer

given
salt:sugar:water
1:8:200
sugar/water = 8/200 * 1/2 ; 1/50
salt/sugar ; 1/8 * 3 ; 3/8
3x/8= 5
x= 40/3
sugar ; 40*50/3 = 2000/3 IMO C ; 666 2/3

GloryBoy92 · Answer

When "the salt ratio is trippled" why do we get 3/8 instead of 1/24?

Similarly with halving the sugar to water ratio. Why sis you get 1/50 instead of 8/100?

Best

stne · Answer

Hi  GloryBoy92 ,

Lets say we have a number 3 , now we want to triple it or increase it. What do we do ? We multiply don't we? We do 3*3 to get 9
Now lets say we want to decease the same number to half its value, what do we do , we divide by 2 don't we hence we have  \frac{3}{2} 
Now lets says we wanted to make the same number even smaller or reduce to  \frac{1}{3}  of its value , what do we do ? we divide by 3 don't we, to get  \frac{3}{3} =1

Hence to increase a number ( Ratio in this case ) we have to multiply and to decrease a number ( Ratio in this case)we
 have to divide.

Similarly Sugar to water ratio is  \frac{8}{200} we want to make it half or decrease it hence as shown above we have to divide by 2 to get  \frac{8}{400}  which when reduced gives  \frac{1}{50} 
What you are doing is multiplying  \frac{8}{200} *2 =  \frac{8}{100}  but this operation is increasing the number instead of decreasing it.
In the same way we have a number  \frac{1}{8}  now we want to triple it or increase it , What do we do? like the first case above we multiply by 3 don't we? hence we do  \frac{1}{8} *3 to get  \frac{3}{8} 
If we wanted to decrease  \frac{1}{8}  to  \frac{1}{3}  of its value then we needed to divide  \frac{1}{8}  by 3 to get  \frac{1}{24} .This is what you were doing.

Hope this answer's your question, please fee free to ask if anything is still unclear.Thanks.

legacyhope · Answer

when you halve the ratio of sugar to water why is the ratio 8:400 and not 4:100 since I am assuming we muliply 1/2 on both sides of the ratio

Bunuel · Answer

Halving the ratio means multiplying the ratio by 1/2, so halving 8/200 becomes 8/200 * 1/2 = 8/400.

A certain electrolyte solution contains 1 gram of salt for every 8 gra

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A certain electrolyte solution contains 1 gram of salt for every 8 gra

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