The ratio of boys to girls in a math class is 5 to 3. When 3 girls and 1 boy join the class, the ratio becomes 4:3. What is the least possible number of students in the class after the new students join?
let number of boys be 5x
let numbe of girls be 3x
after change:
boys --- 5x+1
girls --- 3x+3
(5x+1)/(3x+3) = 4/3
15x + 3 = 12x + 12
3x = 9
x = 3
new class :
boys = 16
girls = 12
total = 28
To solve this problem, we can start by assuming that the initial number of boys and girls in the math class is 5x and 3x, respectively, since the ratio is given as 5 to 3.
After 3 girls and 1 boy join the class, the number of boys becomes 5x + 1, and the number of girls becomes 3x + 3. We are told that the new ratio is 4 to 3.
Based on this, we can set up the following equation:
(5x + 1) / (3x + 3) = 4 / 3
To simplify the equation, we can cross-multiply:
3(5x + 1) = 4(3x + 3)
15x + 3 = 12x + 12
Next, we can subtract 12x from both sides:
15x - 12x + 3 = 12 - 12x + 12
3x + 3 = 12
Then, we can subtract 3 from both sides:
3x + 3 - 3 = 12 - 3
3x = 9
Finally, we can divide both sides of the equation by 3:
3x / 3 = 9 / 3
x = 3
Since x represents the number of students in the original ratio, we can substitute x back into the original ratio to find the number of boys and girls:
Number of boys = 5x = 5 * 3 = 15
Number of girls = 3x = 3 * 3 = 9
Therefore, the original number of students in the math class before the new students joined is 15 + 9 = 24.
After the new students join (3 girls and 1 boy), the minimum number of students in the class is 24 + 3 + 1 = 28.
So, the least possible number of students in the class after the new students join is 28.