Question

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.

Answer 1

I think you just need to setup two equations and solve

Answer 2

@GG1997

Answer 3

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

Answer 4

well how do you do that

Answer 5

and I'm positive it's not a typo

Answer 6

idk looks i have problem interpreting the question lol

Answer 7

Lets start by labeling anyways

let \(a\) = number of adults
\(m\) = number of male students
\(f\) = number of female students

Answer 8

`The number of male students was 1 more than 7 times the number of adults.`

translates to
\[m = 7a+1\tag{1}\]

Answer 9

`The number of female students was half the number of male students`

translates to
\[f=\frac{m}{2}\tag{2}\]

Answer 10

`the total number of people who went on the trip is 82`

translates to
\[a+m+f = 82\tag{3}\]

Answer 11

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

Answer 12

still struggling

Answer 13

lol I really suck at math

Answer 14

basically we have 3 equations and we need to solve 3 unknowns : \(a, m, f\)

Answer 15

ok how

Answer 16

\[m = 7a+1\tag{1}\]
\[f=\frac{m}{2}\tag{2}\]
\[a+m+f = 82\tag{3}\]

rearranging second equation gives, \(m=2f\)
plug this in the remaining equations

Answer 17

\[2f = 7a+1\tag{4}\]
\[a+2f+f=82\tag{5}\]

can you solve this new two equation system with two unknowns ?

Answer 18

do i didvide both sides by 2

Answer 19

You could do that if you want to use substitution

Answer 20

\[2f=7a+1\]
dividing 2 both sides gives
\[f=\dfrac{7a+1}{2}\]

you want to plug this in the other equation and solve \(a\) is it ?

Answer 21

that works, do it

Answer 22

still here ? @GG1997

Answer 23

yes I'm here