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) About Me  (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 5x%2B3=6%2A%28x-2%29 was fully solved.
  • Text form: 5x+3=6*(x-2) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+5x%2B3=6%2A%28x-2%29+%29
    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 5%2Ax%2B3=highlight_red%28+6%2A%28x-2%29+%29.
Moved these terms to the left highlight_green%28+-6%2A%28x-2%29+%29
It becomes 5%2Ax%2B3-highlight_green%28+6%2A%28x-2%29+%29=0.
Look at 5%2Ax%2Bhighlight_red%28+3+%29-6%2A%28x-2%29=0.
Moved 3 to the right of expression
It becomes 5%2Ax-6%2A%28x-2%29%2Bhighlight_green%28+3+%29=0.
Look at 5%2Ax-highlight_red%28+6%2A%28x-2%29+%29%2B3=0.
Expanded term -6 by using associative property on %28x-2%29
It becomes 5%2Ax-highlight_green%28+6%2Ax+%29%2Bhighlight_green%28+6%2A2+%29%2B3=0.
Look at 5%2Ax-6%2Ax%2Bhighlight_red%28+6+%29%2Ahighlight_red%28+2+%29%2B3=0.
Multiplied numerator integers
It becomes 5%2Ax-6%2Ax%2Bhighlight_green%28+12+%29%2B3=0.
Look at 5%2Ax-6%2Ax%2Bhighlight_red%28+12+%29%2Bhighlight_red%28+3+%29=0.
Added fractions or integers together
It becomes 5%2Ax-6%2Ax%2Bhighlight_green%28+15+%29=0.
Look at highlight_red%28+5%2Ax+%29-highlight_red%28+6%2Ax+%29%2B15=0.
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 highlight_green%28+%285-6%29%2Ax+%29%2B15=0.
Look at %28highlight_red%28+5+%29-highlight_red%28+6+%29%29%2Ax%2B15=0.
Added fractions or integers together
It becomes %28highlight_green%28+-1+%29%29%2Ax%2B15=0.
Look at %28highlight_red%28+-1+%29%29%2Ax%2B15=0.
Removed extra sign in front of -1
It becomes %28-highlight_green%28+1+%29%29%2Ax%2B15=0.
Look at highlight_red%28+%28-highlight_red%28+1+%29%29%2Ax+%29%2B15=0.
Remove unneeded parentheses around factor highlight_red%28+1+%29
It becomes -highlight_green%28+1+%29%2Ax%2B15=0.
Look at -highlight_red%28+1+%29%2Ax%2B15=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes -x%2B15=0.
Look at highlight_red%28+-x%2B15+%29=0.
Solved linear equation highlight_red%28+-x%2B15=0+%29 equivalent to -x+15 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
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: 5%2A%2815%29%2B3 simplifies to 78
  • Text form: 5*(15)+3 simplifies to 78
  • Cartoon (animation) form: simplify_cartoon%28+5%2A%2815%29%2B3+%29
    For tutors: simplify_cartoon( 5*(15)+3 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+5%2A%28highlight_red%28+15+%29%29+%29%2B3.
Remove unneeded parentheses around factor highlight_red%28+15+%29
It becomes 5%2Ahighlight_green%28+15+%29%2B3.
Look at highlight_red%28+5+%29%2Ahighlight_red%28+15+%29%2B3.
Multiplied numerator integers
It becomes highlight_green%28+75+%29%2B3.
Look at highlight_red%28+75+%29%2Bhighlight_red%28+3+%29.
Added fractions or integers together
It becomes highlight_green%28+78+%29.
Result: 78

Universal Simplifier and Solver


Done!

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


YOUR ANSWER


  • Graphical form: 6%2A%2815-2%29 simplifies to 78
  • Text form: 6*(15-2) simplifies to 78
  • Cartoon (animation) form: simplify_cartoon%28+6%2A%2815-2%29+%29
    For tutors: simplify_cartoon( 6*(15-2) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 6%2A%28highlight_red%28+15+%29-highlight_red%28+2+%29%29.
Added fractions or integers together
It becomes 6%2A%28highlight_green%28+13+%29%29.
Look at highlight_red%28+6%2A%28highlight_red%28+13+%29%29+%29.
Remove unneeded parentheses around factor highlight_red%28+13+%29
It becomes 6%2Ahighlight_green%28+13+%29.
Look at highlight_red%28+6+%29%2Ahighlight_red%28+13+%29.
Multiplied numerator integers
It becomes highlight_green%28+78+%29.
Result: 78

Universal Simplifier and Solver


Done!

Therefore there are 78 people at the camp.