Original number of boys = 52% of 825 = 0.52 × 825 = 429
Let the number of boys who joined be x
New number of boys = 429 + x
New total students = 825 + x
Set up the equation:
(429 + x) / (825 + x) = 0.64
Multiply both sides by (825 + x):
429 + x = 0.64(825 + x)
Expand:
429 + x = 528 + 0.64x
Subtract 0.64x from both sides:
429 + 0.36x = 528
Subtract 429:
0.36x = 99
Divide by 0.36:
x = 99 / 0.36 = 275
Answer: 275 boys joined the school.