SOLUTION: There are 357 seniors in Harris High School. The ratio of boys to girls is 7:10. How many boys are in the senior class? 210 147 117 107

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: There are 357 seniors in Harris High School. The ratio of boys to girls is 7:10. How many boys are in the senior class? 210 147 117 107       Log On


   

Question 171811: There are 357 seniors in Harris High School. The ratio of boys to girls is 7:10. How many boys are in the senior class?
210
147
117
107
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=# of boys and y=# of girls

Because "There are 357 seniors", this means that x%2By=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%2F10=x%2Fy


7%2F10=x%2Fy Start with the given equation


7%2F10=x%2F%28357-x%29 Plug in y=357-x


7%28357-x%29=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=%28-2499%29%2F%28-17%29 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


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Answer:

So there are 147 boys and 210 girls