Question

Sam needs a 20% acid solution, but she has only an 18% solution and a 25% solution. She decides to use 100 ml of the 18% solution, and she needs to know how much of the 25% solution she should add. The equation 18+0.25x = 0.2 represents this situation, where x represents the millilitres of the 25% solution that 100+x should be added.

How many millilitres should Sam add?
Enter your answer as a number, like this: 42

Answer 1

Sam needs to add 40 ml of the 25% acid solution to 100 ml of her 18% acid solution to create a 20% acid solution.

Step-by-step explanation:

Sam needs to make a 20% acid solution and has 100 ml of an 18% solution to start with. To find out how much of the 25% solution she needs to add, we need to set up an equation that relates the volumes and concentrations of the two solutions to achieve the desired 20% concentration. Using the equation of a mixture C1V1 + C2V2 = Cfinal(V1 + V2), where C represents concentrations and V represents volumes, we can plug in the known values:

• C1 = 18% or 0.18
• V1 = 100 ml (volume of the 18% solution)
• C2 = 25% or 0.25 (concentration of the second solution to be added)
• Cfinal = 20% or 0.20 (desired final concentration)

Rewriting the equation in terms of x, the volume of the 25% solution to be added, we get:

0.18(100) + 0.25x = 0.20(100 + x)

Solving for x:

18 + 0.25x = 20 + 0.2x

0.05x = 2

x = 40 ml

Thus, Sam should add 40 ml of the 25% solution to achieve a 20% acid solution.