Let's start by creating an equation to represent this problem. A total of 85 people can fit in the conference room, but 3 of them will be the principal and counselors. The number of students and parents will be equal to the seating capacity minus the principal and counselors.
85−3
If we let x represent the number of students, and we know each student will bring one parent to the meeting, the number of students and parents combined will be 2x. If the number of students and parents is equal to (85−3) and is also equal to 2x, we get an equation!
(85−3)=2x
To solve this equation, we need to find out for what value(s) of x the equation will remain equal. We should simplify both sides of the equation as much as possible before we try to deduce the value(s) that make the equation hold true.
If we stop here, we can see that both sides of the equation have been simplified as much as possible. What number can be multiplied by 2 and equal 82?
2(41)=2x
For the equation to remain true, x must be equal to 41.
Alternative Solution
A different approach
The meeting will be organized in a room with a max capacity of 85 people. In this meeting, one principal and two counselors will attend which means they will occupy 3 of the seats in the conference room.
85−3=82seats
Each student must bring a parent, so for each student we have to count 2 places, one for the student and one for the parent. If we divide the number of seats which are left by 2, we will get the number of students who can attend the meeting.
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