## 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

I think you just need to setup two equations and solve

2. ganeshie8

@GG1997

3. ganeshie8

are you really sure the work adult was not a typo ?

4. anonymous

well how do you do that

5. anonymous

and I'm positive it's not a typo

6. ganeshie8

idk looks i have problem interpreting the question lol

7. ganeshie8

Lets start by labeling anyways let $$a$$ = number of adults $$m$$ = number of male students $$f$$ = number of female students

8. ganeshie8

The number of male students was 1 more than 7 times the number of adults. translates to $m = 7a+1\tag{1}$

9. ganeshie8

The number of female students was half the number of male students translates to $f=\frac{m}{2}\tag{2}$

10. ganeshie8

the total number of people who went on the trip is 82 translates to $a+m+f = 82\tag{3}$

11. ganeshie8

so we have a system with 3 equations, knw how to solve ?

12. anonymous

still struggling

13. anonymous

lol I really suck at math

14. ganeshie8

basically we have 3 equations and we need to solve 3 unknowns : $$a, m, f$$

15. anonymous

ok how

16. 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

17. ganeshie8

$2f = 7a+1\tag{4}$ $a+2f+f=82\tag{5}$ can you solve this new two equation system with two unknowns ?

18. anonymous

do i didvide both sides by 2

19. ganeshie8

You could do that if you want to use substitution

20. 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 ?

21. ganeshie8

that works, do it

22. ganeshie8

still here ? @GG1997

23. anonymous

yes I'm here