SOLUTION: In the group of students who voted in a Year 9 school leader election, the ratio of girls to boys is 2 : 3. If 10 more girls and 5 more boys had voted, the ratio would have been 3

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: In the group of students who voted in a Year 9 school leader election, the ratio of girls to boys is 2 : 3. If 10 more girls and 5 more boys had voted, the ratio would have been 3       Log On


   

Question 967599: In the group of students who voted in a Year 9 school leader election, the ratio of girls to boys is 2 : 3. If 10 more girls and 5 more boys had voted, the ratio would have been 3 : 4. How many students voted altogether?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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In the group of students who voted in a Year 9 school leader election, the ratio of girls to boys is 2 : 3.
Let x = the multiplier
then
2x = no. of girls
and
3x = no. of boys
also
5x = total students
:
If 10 more girls and 5 more boys had voted, the ratio would have been 3 : 4.
%28%282x%2B10%29%29%2F%28%283x%2B5%29%29 = 3%2F4
Cross multiply and find x
3(3x+5) = 4(2x+10)
9x + 15 = 8x + 40
9x - 8x = 40 - 15
x = 25 is the multiplier
:
How many students voted altogether?
5(25) = 125 total students