Question 171811
Let x=# of boys and y=# of girls


Because "There are 357 seniors", this means that {{{x+y=357}}}. Solving for "y", we get {{{y=357-x}}}



Since "The ratio of boys to girls is 7:10", this tells us that we have the ratio:


{{{7/10=x/y}}}



{{{7/10=x/y}}} Start with the given equation



{{{7/10=x/(357-x)}}} Plug in {{{y=357-x}}}



{{{7(357-x)=10x}}} Cross multiply



{{{2499-7x=10x}}} Distribute.



{{{-7x=10x-2499}}} Subtract {{{2499}}} from both sides.



{{{-7x-10x=-2499}}} Subtract {{{10x}}} from both sides.



{{{-17x=-2499}}} Combine like terms on the left side.



{{{x=(-2499)/(-17)}}} Divide both sides by {{{-17}}} to isolate {{{x}}}.



{{{x=147}}} Reduce. So there are 147 boys



{{{y=357-x}}} Go back to the isolated equation



{{{y=357-147}}} Plug in {{{x=147}}}



{{{y=210}}} Subtract. So there are 210 girls



----------------------------------------------------------------------


Answer:


So there are 147 boys and 210 girls