Question 1175686

the ratio of boys to girls in a group is 3:4. if 6 more boys join the group and 6 girls leave the group the ratio becomes 4:3. How many girls were originally in the group? 
<pre>Let multiplicative factor be x
Then original number of boys and girls = 3x, and 4x, respectively
Then we get: {{{matrix(1,3, (3x + 6)/(4x - 6), "=", 4/3)}}}
3(3x + 6) = 4(4x - 6) ------ Cross-multiplying
9x + 18 = 16x - 24
9x - 16x = - 24 - 18
- 7x = - 42
Multiplicative factor, or {{{matrix(1,5, x, "=", (- 42)/(- 7), "=", 6)}}}
Original number of girls: {{{highlight_green(matrix(1,5, 4x, "=", 4(6), "=", highlight(24)))}}}
That's all! Nothing MORE, nothing LESS!!