anonymous
  • anonymous
A group of adults and students went on a class trip to Washington, DC. The number of male students was 1 more than 7 times the number of adults. The number of female students was half the number of male students. If the total number of people who went on the trip is 82, find the numbers of male students and female students.
Mathematics
jamiebookeater
  • jamiebookeater
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ganeshie8
  • ganeshie8
I think you just need to setup two equations and solve
ganeshie8
  • ganeshie8
ganeshie8
  • ganeshie8
are you really sure the work `adult` was not a typo ?

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anonymous
  • anonymous
well how do you do that
anonymous
  • anonymous
and I'm positive it's not a typo
ganeshie8
  • ganeshie8
idk looks i have problem interpreting the question lol
ganeshie8
  • ganeshie8
Lets start by labeling anyways let \(a\) = number of adults \(m\) = number of male students \(f\) = number of female students
ganeshie8
  • ganeshie8
`The number of male students was 1 more than 7 times the number of adults.` translates to \[m = 7a+1\tag{1}\]
ganeshie8
  • ganeshie8
`The number of female students was half the number of male students` translates to \[f=\frac{m}{2}\tag{2}\]
ganeshie8
  • ganeshie8
`the total number of people who went on the trip is 82` translates to \[a+m+f = 82\tag{3}\]
ganeshie8
  • ganeshie8
so we have a system with 3 equations, knw how to solve ?
anonymous
  • anonymous
still struggling
anonymous
  • anonymous
lol I really suck at math
ganeshie8
  • ganeshie8
basically we have 3 equations and we need to solve 3 unknowns : \(a, m, f\)
anonymous
  • anonymous
ok how
ganeshie8
  • ganeshie8
\[m = 7a+1\tag{1}\] \[f=\frac{m}{2}\tag{2}\] \[a+m+f = 82\tag{3}\] rearranging second equation gives, \(m=2f\) plug this in the remaining equations
ganeshie8
  • ganeshie8
\[2f = 7a+1\tag{4}\] \[a+2f+f=82\tag{5}\] can you solve this new two equation system with two unknowns ?
anonymous
  • anonymous
do i didvide both sides by 2
ganeshie8
  • ganeshie8
You could do that if you want to use substitution
ganeshie8
  • ganeshie8
\[2f=7a+1\] dividing 2 both sides gives \[f=\dfrac{7a+1}{2}\] you want to plug this in the other equation and solve \(a\) is it ?
ganeshie8
  • ganeshie8
that works, do it
ganeshie8
  • ganeshie8
still here ? @GG1997
anonymous
  • anonymous
yes I'm here

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