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Question

Difficulty: EasyRatios, Rates, and Proportions

In a school election for student council president, the ratio of the number of votes received by Candidate A to the number of votes received by Candidate B was 2:32:3. If Candidate B received 120120 votes, how many votes did Candidate A receive?

  1. A
    48
  2. B
    72
  3. 80Answer
  4. D
    180
  5. E
    200

Answer

Candidate A received 80 votes.
The ratio of the number of votes for Candidate A to Candidate B is 2:32:3. Since Candidate B received 120120 votes, we can set up the proportion Votes for A120=23\frac{\text{Votes for A}}{120} = \frac{2}{3}. Multiplying both sides by 120120 gives Votes for A=120×23=80\text{Votes for A} = 120 \times \frac{2}{3} = 80.

Step-by-Step Solution

1
Identify the given ratio and values.
The ratio of Candidate A's votes to Candidate B's votes is 2:32:3, and Candidate B received 120120 votes.
This sets up the proportion relationship where the ratio of Candidate A's votes to Candidate B's votes is equal to 2 to 3.
2
Set up a proportion to solve for Candidate A's votes.
x120=23\frac{x}{120} = \frac{2}{3}, where xx represents the number of votes Candidate A received.
This equates the simplified ratio of votes to the actual number of votes.
3
Solve for xx by multiplying both sides by 120120.
x=120×23=80x = 120 \times \frac{2}{3} = 80.
This isolates the variable xx to find the correct number of votes Candidate A received.

Key Concept

Solving proportions and scaling ratios based on a given part.
Estimated Time:45s
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Topics

Ratios, Rates, and Proportions

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