A chemist has two alcohol solutions of different strength, 30% alcohol and 45% alcohol solutions, respectively. How many cubic centimeters of each must he use so as to make a mixture of 30 cubic centimeters which will contain 39% alcohol.

(a)10 and 20 

(b)6 and 24

(c)12 and 18 

(d)15 and 15

Ans:

Given:

Two alcohol solutions: 30% and 45% alcohol solutions.

Mixture volume: 30 cubic centimeters.

Target alcohol concentration in the mixture: 39%.

Let:

( x ) be the volume (in cubic centimeters) of the 30% alcohol solution.

( y ) be the volume (in cubic centimeters) of the 45% alcohol solution.

Step 1: Write the Equations based on the Mixture:

The total volume of the mixture is 30 cubic centimeters: ( x + y = 30 ) (Equation 1).

The total amount of alcohol in the mixture is 39% of 30 cubic centimeters: ( 0.30x + 0.45y = 0.39 \times 30 ) (Equation 2).

Step 2: Solve the Equations:

From Equation 1, we have ( x = 30 - y ).

Substitute ( x ) in Equation 2: ( 0.30(30 - y) + 0.45y = 11.7 ).

Simplify the equation: ( 9 - 0.30y + 0.45y = 11.7 ).

Further simplify: ( 0.15y = 2.7 ) and ( y = 18 ).

Substitute ( y = 18 ) in ( x = 30 - y ): ( x = 12 ).

Step 3: Check the Solution:

The chemist should use 12 cubic centimeters of the 30% alcohol solution and 18 cubic centimeters of the 45% alcohol solution to make a 30 cubic centimeter mixture with 39% alcohol content.

Therefore, the correct answer is (c) 12 and 18.