Question

10 mark q review
a chemist mixed a liters of a 2% saline solution with y liters of a 7% saline solution to
produce a 4% saline solution. which equation best represents this mixture? (assume the
volumes of the solutions are additive.)
(a) ( 0.02 x + 0.07 y = 4 ( x + y ) )
(b) ( 0.02 x + 0.07 y = 0.04 ( x + y ) )
(c) ( 0.2 x + 0.7 y = 4 ( x + y ) )
(d) ( 0.2 x + 0.7 y = 0.4 ( x + y ) )

Explanation:

Step1: Calculate the amount of solute in each solution

The amount of solute in \(x\) liters of \(2\%\) solution is \(0.02x\) (since \(2\%=\frac{2}{100} = 0.02\)).
The amount of solute in \(y\) liters of \(7\%\) solution is \(0.07y\) (since \(7\%=\frac{7}{100}=0.07\)).
The total volume of the new solution is \((x + y)\) liters, and the new solution is \(4\%\) ，so the amount of solute in the new solution is \(0.04(x + y)\) (since \(4\%=\frac{4}{100}=0.04\)).

Step2: Set up the equation

By the conservation of the amount of solute (the sum of solutes in the two original solutions equals the solute in the new solution), we have the equation \(0.02x+0.07y = 0.04(x + y)\).

Answer:

A. \(0.02x + 0.07y=0.04(x + y)\)