The total number of pairs that can be formed with the given teams is 6. After increasing the team sizes by 5 developers while maintaining the same ratio, the new distribution will be: Alpha - 31, Beta - 27, Gamma - 20, Delta - 18. The total number of developers in the company will be 96. Team Gamma will receive $20,833.33 in funding based on the current developer ratio.
Part 1: In order to determine how many pairs can be formed, we need to calculate the number of possible combinations. Each team needs to be paired with another team, so we will use the formula for combinations:
C(n, 2) = n! / (2! * (n-2)!)
where n is the number of teams.
C(4, 2) = 4! / (2! * (4-2)!) = 6
Therefore, a total of 6 pairs can be formed.
Part 2: If each team's size increases by 5 developers while maintaining the same ratio, we can calculate the new distribution. We first calculate the total number of developers:
Total developers = Number of developers in Alpha + Number of developers in Beta + Number of developers in Gamma + Number of developers in Delta
Total developers = 30 + 25 + 20 + 15 = 90
Then, we calculate the new distribution:
Alpha: (30 + 5)/(90 + 4 * 5) * 90 = 35/110 * 90 = 31
Beta: (25 + 5)/(90 + 4 * 5) * 90 = 30/110 * 90 = 27
Gamma: (20 + 5)/(90 + 4 * 5) * 90 = 25/110 * 90 = 20
Delta: (15 + 5)/(90 + 4 * 5) * 90 = 20/110 * 90 = 18
Therefore, the new distribution of developers is: Alpha: 31, Beta: 27, Gamma: 20, Delta: 18. The total number of developers in the company is 31 + 27 + 20 + 18 = 96.
Part 3: To determine the amount of funding Team Gamma will receive, we need to calculate the proportion of developers in Gamma relative to the total number of developers:
Proportion of developers in Gamma = Number of developers in Gamma / Total number of developers = 20/96
Given that the total funding is $100,000, the amount of funding Team Gamma will receive is:
Funding for Team Gamma = Proportion of developers in Gamma * Total funding = (20/96) * $100,000 = $20,833.33
The probable question may be:
In a tech company with four software development teams (Team Alpha, Beta, Gamma, and Delta), the number of developers in each team forms a ratio. The current distribution is as follows:
Team Number of Developers
Alpha 30
Beta 25
Gamma 20
Delta 15
Part 1: If each team needs to form pairs to work on a collaborative project, how many pairs can be formed in total?
Part 2: The company is planning to hire additional developers for each team, maintaining the same ratio. If each team's size increases by 5 developers, what will be the new distribution of developers, and how many developers will be in the company altogether?
Part 3: If the company decides to allocate additional resources to the teams based on the ratio of their current sizes, such that each team receives funding in proportion to the number of developers, determine the amount of funding Team Gamma will receive if the total funding is $100,000.