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?

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?      Log On


   

Question 164991: 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?
Answer by jim_thompson5910(35256) About Me  (Show Source):
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Let x=# of boy seniors and y=# of girl seniors


Since there are 357 seniors, this means that x%2By=357


y=357-x Subtract x from both sides to solve for y


Now the ratio 7:10 can be written as the fraction 7%2F10. Also, the ratio of x boys to y girls is x%2Fy. Since these two ratios are equivalent, this tells us that x%2Fy=7%2F10


x%2Fy=7%2F10 Start with the previous ratio


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


10x=7%28357-x%29 Cross multiply


10x=2499-7x Distribute.


10x%2B7x=2499 Add 7x to both sides.


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


x=%282499%29%2F%2817%29 Divide both sides by 17 to isolate x.


x=147 Reduce. So this means that there are 147 boys in the senior class


y=357-x Go back to the previously isolated equation


y=357-147 Plug in x=147


y=210 Subtract. So there are 210 girls in the senior class


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Answer:


There are 147 boys and 210 girls in the senior class


Note: the ratio of 147 boys to 210 girls reduces to 7 boys to 10 girls