Answer: 75 boys
Explanation:
Let's start by assuming that the total number of members on the math team at the beginning of the year is represented by the variable "x".
From the given information, we know that initially, 3/5 of x members were girls. So, the number of girls at the beginning of the year can be calculated as (3/5) * x.
After 5 more girls joined, the number of girls becomes [(3/5) * x] + 5.
The ratio of girls to boys is given as 2:1. This means that the number of girls is twice the number of boys.
We can set up the equation: [(3/5) * x] + 5 = 2 * (1/3) * x.
To solve for x, we can simplify the equation:
(3/5) * x + 5 = (2/3) * x.
To get rid of the fractions, we can multiply both sides of the equation by 15 (the least common multiple of 5 and 3):
15 * [(3/5) * x + 5] = 15 * [(2/3) * x].
This simplifies to:
9x + 75 = 10x.
Now, we can solve for x:
75 = 10x - 9x,
75 = x.
So, there were 75 boys on the math team at the beginning of the year.
In conclusion, there were 75 boys on the math team at the beginning of the year.