Question
In a class, the ratio of the number of boys to the
number of girls is 9:7. If 3 boys joined the class and 2 girls left the class, then the ratio becomes 7:4. Find the original number of girls in the class.Solution
Let initially the number of boys and girls be 9x and 7x, respectively. After 3 boys join and 2 girls leave, the numbers are (9x + 3) for boys and (7x - 2) for girls. The new ratio is given as 7:4. Setting up the equation, 4(9x + 3) = 7(7x - 2) simplifies to 36x + 12 = 49x - 14. Solving for x, we get 13x = 26, so x = 2. Therefore, the number of girls initially was 7x = 7 * 2 = 14.
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