Question

after 12 girls left the school assembly the ratio of the number of boys to girls is 3 to 4. if there were w boys at the assembly, write an algebraic expression for the number of girls at the beginning of the assembly in terms of w

Answer 1

Let g = original # of girls at the assembly.
Let w = # of boys at the assembly.

Equation of ratios:

w                 3         boys
-------    =    ---- = --------------------------------------------
g-12             4      girls after 12 have left assembly
                                                                                     4w + 36
Cross-mult., 4w = 3g - 36, so 4w + 36 = 3g, and g = ---------------  (answer)
                                                                                           4

This is "original # of girls at the assembly in terms of w, the # of boys at the assembly."