SOLUTION: At a school camp 5 people could be accommodated per room but 3 people leftover.if each room had 6 people, 2 rooms would be left over. How many students attended the camp?

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Question 1012100: At a school camp 5 people could be accommodated per room but 3 people leftover.if each room had 6 people, 2 rooms would be left over. How many students attended the camp?
Answer by ValorousDawn(53)   (Show Source): You can put this solution on YOUR website!
Lets say there are an x number of rooms.
5x+3=6(x-2)
The two sides of the equation represent the number of people. If each room can fit 5 people, and there are an x number of rooms, there are 5x people, but with 3 leftover, so we add 3. The right side has x-2 in parenthesis, because there are 2 fewer rooms, but we change the 5 to a 6, as there are now 6 people a room.
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=15.
  • Graphical form: Equation was fully solved.
  • Text form: 5x+3=6*(x-2) simplifies to 0=0
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( 5x+3=6*(x-2) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION


Look at .
Moved these terms to the left highlight_green%28+-6%2A%28x-2%29+%29
It becomes .

Look at .
Moved 3 to the right of expression
It becomes .

Look at .
Expanded term -6 by using associative property on %28x-2%29
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
Added fractions or integers together
It becomes .

Look at .
Eliminated similar terms highlight_red%28+5%2Ax+%29,highlight_red%28+-6%2Ax+%29 replacing them with highlight_green%28+%285-6%29%2Ax+%29
It becomes .

Look at .
Added fractions or integers together
It becomes .

Look at .
Removed extra sign in front of -1
It becomes .

Look at .
Remove unneeded parentheses around factor highlight_red%28+1+%29
It becomes .

Look at .
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes .

Look at .
Solved linear equation highlight_red%28+-x%2B15=0+%29 equivalent to -x+15 =0
It becomes .
Result:
This is an equation! Solutions: x=15.

Universal Simplifier and Solver


Done!

With 15 people per room, you can plug it into either equation to find the number of people.
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: simplifies to
  • Text form: 5*(15)+3 simplifies to 78
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( 5*(15)+3 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION


Look at .
Remove unneeded parentheses around factor highlight_red%28+15+%29
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
Added fractions or integers together
It becomes .
Result:

Universal Simplifier and Solver


Done!

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: simplifies to
  • Text form: 6*(15-2) simplifies to 78
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( 6*(15-2) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION


Look at .
Added fractions or integers together
It becomes .

Look at .
Remove unneeded parentheses around factor highlight_red%28+13+%29
It becomes .

Look at .
Multiplied numerator integers
It becomes .
Result:

Universal Simplifier and Solver


Done!

Therefore there are 78 people at the camp.

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