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

Answer 1

The resulting solution contains approximately 666 g of water.

Step-by-step explanation:

In the initial solution we have:

1g salt : 8g sugar : 200g water

This means that the ratios are:

`(salt)/(sugar)  = (1)/(8) \\\\(sugar)/(water) = (8)/(200) =(1)/(25)`

In the final solution we have:

5g salt: xg sugar: yg water

The new ratios are:

`(salt)/(sugar) = (3)/(8) \\\\(sugar)/(water) = (1)/(50)`

Now we can calculate the amount of sugar in the final solution:

`(salt)/(sugar)  = (5)/(x) =(3)/(8) \\\\X = 13.333 g`

Finally, we calculate the amount of water:

`(sugar)/(water) = (13.333)/(y) = (1)/(50) \\y = 666.667 g`