Team Alpha had one fourth as many people as team Beta. After 6 people quit team Beta and 12 people were transferred to team Alpha from team Beta, both teams became equal. How many people were there originally on team Alpha?
A = B / 4
B - 6 - 12 = A + 12 ... B = A + 30
solve the system
i still don't get how to get the answer
just give the dam answer
Team Alpha had one fourth as many people as team Beta. After 6 people quit team Beta and 12 people were transferred to team Alpha from team Beta, both teams became equal. How many people were there originally on team Alpha?
To solve this problem, let's break it down step by step:
Let's assume the initial number of people on team Alpha was A, and the initial number of people on team Beta was B.
Given the information, we can write two equations:
Equation 1: A = (1/4)B (Team Alpha had one fourth as many people as team Beta)
Equation 2: A + 12 = B - 6 (After 6 people quit team Beta and 12 people were transferred to team Alpha from team Beta, both teams became equal)
To find the original number of people on team Alpha, we need to solve these equations simultaneously.
Let's start by substituting Equation 1 into Equation 2:
(1/4)B + 12 = B - 6
To eliminate the fraction, we can multiply both sides of the equation by 4:
B + 48 = 4B - 24
Bringing the terms with B to one side:
4B - B = 48 + 24
3B = 72
Dividing both sides by 3:
B = 24
Now that we know B, we can substitute it back into Equation 1 to find A:
A = (1/4)B
A = (1/4) * 24
A = 6
Therefore, the original number of people on team Alpha was 6.