To determine the number of votes that candidate A received, we need to carefully examine the given ratio and total votes.
We are told that candidates A and B received votes in a ratio of 2:3 and that the total number of votes is 360.
Here is a detailed, step-by-step solution:
1. Understand the ratio: The ratio 2:3 means that for every 5 parts (2 parts for A and 3 parts for B), the parts are divided into 2 parts for A and 3 parts for B.
2. Total parts: The total number of parts is the sum of the parts for candidates A and B. This is [tex]\(2 + 3 = 5\)[/tex] parts.
3. Votes for candidate A:
- Candidate A receives 2 parts out of 5.
- To find the number of votes candidate A gets, we multiply the fraction of parts candidate A receives by the total number of votes.
- This gives us:
[tex]\[
\text{Votes for candidate A} = \left(\frac{2}{5}\right) \times 360
\][/tex]
4. Calculating the votes:
[tex]\[
\text{Votes for candidate A} = \left(\frac{2}{5}\right) \times 360 = 144
\][/tex]
Therefore, candidate A received 144 votes.
To summarize, in the election, candidate A received 144 votes from the total of 360 votes, given the ratio of 2:3 between candidate A and candidate B.
