Question

A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. What fraction of the mixture must be drawn off and replaced with liquid which contains 4 parts of water and 3 parts of syrup, so that the mixture may be half water and half syrup? Express your answer as common fraction of number of parts.

Answer 1

Tester,this is the solution to the problem:

Vessel filled initially with:

• 3/8 of water

,

• 5/8 of syrup

Vessel replaced with:

• 4/7 of water

,

• 3/7 of syrup

Vessel finally will have:

• 1/2 of water

,

• 1/2 of syrup

Therefore, we need to:

Let x to represent the fraction of the mixture that must be drawn off.

4/7 - 3x/8 = 1/2

Lowest Common Denominator: 56, therefore:

32 - 21x = 28

-21x = 28 - 32

-21x = -4

Dividing by -21 at both sides:

-21x/-21 = -4/-21

x = 4/21

We need to drawn off 4/21 of the first mixture.