9
algebra

A chemist has a 10% salt solution and a 25% salt solution. How many liters of the 25% solution must be added to 20 liters of the 10% solution to create an 18% solution?

A

18 liters

B

20 liters

C

24 liters

D

30 liters

Correct Answer: B

Choice B is the correct answer. Let xx = liters of 25% solution to add.

Equation: (amount of salt) before mixing = (amount of salt) after mixing 0.10(20)+0.25x=0.18(20+x)0.10(20) + 0.25x = 0.18(20 + x)

Step 1: Expand: 2+0.25x=3.6+0.18x2 + 0.25x = 3.6 + 0.18x

Step 2: Solve: 0.25x0.18x=3.620.25x - 0.18x = 3.6 - 20.07x=1.60.07x = 1.6x=1.60.07=160722.86x = \frac{1.6}{0.07} = \frac{160}{7} \approx 22.86

0.10(20)+0.25(20)=2+5=70.10(20) + 0.25(20) = 2 + 5 = 7 total salt Total solution: 20+20=4020 + 20 = 40 liters Concentration: 740=0.175=17.5%\frac{7}{40} = 0.175 = 17.5\%

2+0.25x=0.18(20+x)2 + 0.25x = 0.18(20 + x)2+0.25x=3.6+0.18x2 + 0.25x = 3.6 + 0.18x0.07x=1.60.07x = 1.6x=22.857...x = 22.857...

💡 Strategic Tip: Mixture problems: concentration × volume = amount of substance.

**Other choices based on calculation.