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anonymous

  • one year ago

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.

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  1. ganeshie8
    • one year ago
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    I think you just need to setup two equations and solve

  2. ganeshie8
    • one year ago
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    @GG1997

  3. ganeshie8
    • one year ago
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    are you really sure the work `adult` was not a typo ?

  4. anonymous
    • one year ago
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    well how do you do that

  5. anonymous
    • one year ago
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    and I'm positive it's not a typo

  6. ganeshie8
    • one year ago
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    idk looks i have problem interpreting the question lol

  7. ganeshie8
    • one year ago
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    Lets start by labeling anyways let \(a\) = number of adults \(m\) = number of male students \(f\) = number of female students

  8. ganeshie8
    • one year ago
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    `The number of male students was 1 more than 7 times the number of adults.` translates to \[m = 7a+1\tag{1}\]

  9. ganeshie8
    • one year ago
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    `The number of female students was half the number of male students` translates to \[f=\frac{m}{2}\tag{2}\]

  10. ganeshie8
    • one year ago
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    `the total number of people who went on the trip is 82` translates to \[a+m+f = 82\tag{3}\]

  11. ganeshie8
    • one year ago
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    so we have a system with 3 equations, knw how to solve ?

  12. anonymous
    • one year ago
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    still struggling

  13. anonymous
    • one year ago
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    lol I really suck at math

  14. ganeshie8
    • one year ago
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    basically we have 3 equations and we need to solve 3 unknowns : \(a, m, f\)

  15. anonymous
    • one year ago
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    ok how

  16. ganeshie8
    • one year ago
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    \[m = 7a+1\tag{1}\] \[f=\frac{m}{2}\tag{2}\] \[a+m+f = 82\tag{3}\] rearranging second equation gives, \(m=2f\) plug this in the remaining equations

  17. ganeshie8
    • one year ago
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    \[2f = 7a+1\tag{4}\] \[a+2f+f=82\tag{5}\] can you solve this new two equation system with two unknowns ?

  18. anonymous
    • one year ago
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    do i didvide both sides by 2

  19. ganeshie8
    • one year ago
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    You could do that if you want to use substitution

  20. ganeshie8
    • one year ago
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    \[2f=7a+1\] dividing 2 both sides gives \[f=\dfrac{7a+1}{2}\] you want to plug this in the other equation and solve \(a\) is it ?

  21. ganeshie8
    • one year ago
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    that works, do it

  22. ganeshie8
    • one year ago
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    still here ? @GG1997

  23. anonymous
    • one year ago
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    yes I'm here

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