Question

In a lab, a 30% acid solution is being mixed with a 5% acid solution to create a 10% acid solution. What is the ratio of the amount of the 30% solution to the amount of 5% solution used to create the 10% solution?

a) 1:3
b) 1:4
c) 1:5
d) 1:6

Answer 1

To create a 10% acid solution, for every 1 part of the 30% acid solution, 4 parts of the 5% acid solution are needed. The mixture equation simplifies to indicate that the ratio of the 30% solution to the 5% solution is 1:4 (b).

Step-by-step explanation:

To find the ratio of the amount of a 30% acid solution to the amount of a 5% acid solution used to make a 10% acid solution, we can use the method of algebraic mixture equations. In this case, we let x be the amount of the 30% solution and y be the amount of the 5% solution. The total amount of pure acid from both solutions should be equal to the amount of acid in the 10% solution.

The mixture equation can be written as follows:
0.30x + 0.05y = 0.10(x + y)

We can simplify this equation by multiplying through by 100 to remove the decimals, which yields:

30x + 5y = 10(x + y)

Before going on, we know that there should be more of the 5% solution than the 30% solution to achieve a 10% solution, which is closer to 5% than to 30%. Solving the equation for y in terms of x:

30x + 5y = 10x + 10y

20x = 5y

y = 4x

The ratio of the amount of 30% solution (x) to the amount of 5% solution (y) is therefore 1:4. Hence, for every 1 part of the 30% solution, 4 parts of the 5% solution are needed. The correct answer is choice b) 1:4.