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

Answer:

The resulting solution contains approximately 666 g of water.

Explanation:

In the initial solution we have:

1g salt : 8g sugar : 200g water

This means that the ratios are:

$\frac{salt}{sugar} = \frac{1}{8} \\\\\frac{sugar}{water} = \frac{8}{200} =\frac{1}{25}$

In the final solution we have:

5g salt: xg sugar: yg water

The new ratios are:

$\frac{salt}{sugar} = \frac{3}{8} \\\\\frac{sugar}{water} = \frac{1}{50}$

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

$\frac{salt}{sugar} = \frac{5}{x} =\frac{3}{8} \\\\X = 13.333 g$

Finally, we calculate the amount of water:

$\frac{sugar}{water} = \frac{13.333}{y} = \frac{1}{50} \\y = 666.667 g$