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Difficulty: HardPercents and Percent Change

A laboratory technician prepared a chemistry solution containing only liquid A and liquid B. Initially, liquid A made up 35%35\% of the total volume of the solution. After 150150 milliliters of liquid B was removed from the solution, the volume of liquid A became 42%42\% of the total volume of the remaining solution. What was the initial volume of liquid A, in milliliters?

  1. 315Answer
  2. B
    378
  3. C
    750
  4. D
    900

Answer

315
The correct answer is 315. Let VV represent the initial total volume of the solution. Initially, liquid A's volume is 0.35V0.35V. After removing 150150 milliliters of liquid B, the total volume becomes V−150V - 150. Since only liquid B was removed, the volume of liquid A remains unchanged. This volume is now 42%42\% of the new total volume, which gives the equation 0.35V=0.42(V−150)0.35V = 0.42(V - 150). Expanding the right side yields 0.35V=0.42V−630.35V = 0.42V - 63. Subtracting 0.35V0.35V and adding 6363 to both sides results in 0.07V=630.07V = 63, which simplifies to V=900V = 900 milliliters. To find the initial volume of liquid A, we calculate 35%35\% of 900900, which is 315315 milliliters.

Step-by-Step Solution

1
Let VV represent the initial total volume of the solution in milliliters. Express the initial volume of liquid A in terms of VV.
The initial volume of liquid A is 0.35V0.35V milliliters.
Liquid A constitutes 35%35\% of the initial total volume VV.
2
Express the final total volume of the solution after removing 150150 milliliters of liquid B.
The final total volume is V−150V - 150 milliliters.
Subtracting the volume of liquid B that was removed from the initial total volume gives the remaining total volume.
3
Set up an equation representing the volume of liquid A in the remaining solution and solve for VV.
0.35V=0.42(V−150)  ⟹  0.35V=0.42V−63  ⟹  0.07V=63  ⟹  V=9000.35V = 0.42(V - 150) \implies 0.35V = 0.42V - 63 \implies 0.07V = 63 \implies V = 900 milliliters.
The volume of liquid A remains constant, but it now represents 42%42\% of the remaining total volume V−150V - 150.
4
Calculate the initial volume of liquid A.
0.35×900=3150.35 \times 900 = 315 milliliters.
Substitute the value of VV back into the expression for the initial volume of liquid A.

Key Concept

Solving multi-step percent problems involving a change in the baseline total volume.
Estimated Time:2m 0s
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Topics

Percents and Percent Change

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