SOLUTION: Hi i need help with a problem im stuck on: A group of 127 students and 4 teachers go on a field trip. They have vans which hold seven students and buss which hold 25. They have fiv

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Question 214968: Hi i need help with a problem im stuck on: A group of 127 students and 4 teachers go on a field trip. They have vans which hold seven students and buss which hold 25. They have five more vans than buses.How many buses and vans are needed.
I said 7v + 25v = 131 and got stuck on this.
Please help
Found 2 solutions by drj, ptaylor:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
A group of 127 students and 4 teachers go on a field trip. They have vans which hold seven students and buss which hold 25. They have five more vans than buses. How many buses and vans are needed.

Step 1. Let x be the number of buses. Let x+5 be the number of vans.

Step 2. Let 7(x+5) be the numbers of students in the vans.

Step 3. Let 25x be the number of students in the buses.

Step 4. 7(x+5)+25x=131 Total number of students and teachers in the buses and vans resulting from adding the expressions in Steps 2 and 3.

Step 5. The following steps will solve the above equation in Step 4.

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


YOUR ANSWER


  • This is an equation! Solutions: x=3.
  • Graphical form: Equation 7%2A%28x%2B5%29%2B25x=131 was fully solved.
  • Text form: 7*(x+5)+25x=131 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+7%2A%28x%2B5%29%2B25x=131+%29
    For tutors: simplify_cartoon( 7*(x+5)+25x=131 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 7%2A%28x%2B5%29%2B25%2Ax=highlight_red%28+131+%29.
Moved these terms to the left highlight_green%28+-131+%29
It becomes 7%2A%28x%2B5%29%2B25%2Ax-highlight_green%28+131+%29=0.
Look at highlight_red%28+7%2A%28x%2B5%29+%29%2B25%2Ax-131=0.
Expanded term 7 by using associative property on %28x%2B5%29
It becomes highlight_green%28+7%2Ax+%29%2Bhighlight_green%28+7%2A5+%29%2B25%2Ax-131=0.
Look at 7%2Ax%2Bhighlight_red%28+7+%29%2Ahighlight_red%28+5+%29%2B25%2Ax-131=0.
Multiplied numerator integers
It becomes 7%2Ax%2Bhighlight_green%28+35+%29%2B25%2Ax-131=0.
Look at 7%2Ax%2Bhighlight_red%28+35+%29%2B25%2Ax-highlight_red%28+131+%29=0.
Added fractions or integers together
It becomes 7%2Ax%2Bhighlight_green%28+-96+%29%2B25%2Ax=0.
Look at 7%2Ax%2Bhighlight_red%28+-96+%29%2B25%2Ax=0.
Moved -96 to the right of expression
It becomes 7%2Ax%2B25%2Ax%2Bhighlight_green%28+-96+%29=0.
Look at 7%2Ax%2B25%2Ax%2Bhighlight_red%28+-96+%29=0.
Removed extra sign in front of -96
It becomes 7%2Ax%2B25%2Ax-highlight_green%28+96+%29=0.
Look at highlight_red%28+7%2Ax+%29%2Bhighlight_red%28+25%2Ax+%29-96=0.
Eliminated similar terms highlight_red%28+7%2Ax+%29,highlight_red%28+25%2Ax+%29 replacing them with highlight_green%28+%287%2B25%29%2Ax+%29
It becomes highlight_green%28+%287%2B25%29%2Ax+%29-96=0.
Look at %28highlight_red%28+7+%29%2Bhighlight_red%28+25+%29%29%2Ax-96=0.
Added fractions or integers together
It becomes %28highlight_green%28+32+%29%29%2Ax-96=0.
Look at highlight_red%28+%28highlight_red%28+32+%29%29%2Ax+%29-96=0.
Remove unneeded parentheses around factor highlight_red%28+32+%29
It becomes highlight_green%28+32+%29%2Ax-96=0.
Look at highlight_red%28+32%2Ax-96+%29=0.
Solved linear equation highlight_red%28+32%2Ax-96=0+%29 equivalent to 32*x-96 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=3.

Universal Simplifier and Solver


Done!




With x=3 , then x+5=8. Check if you have 131 students and teachers by solving 3*25+8*7=75+56=131 which is a true statement.

Step 6. The number of buses is 3 and the number of vans is 8.


I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J


Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!

YOU ARE PRETTY MUCH ON THE RIGHT TRACK---AT LEAST YOU GAVE IT A SHOT.
Let v=number of buses
Then v+5=number of vans
7(v+5)+25v=131
7v+35+25v=131 subtract 35 from each side
32v=131-35
32v=96
v=3--------------------number of buses needed
v+5=3+5=8----------------number of vans needed
CK
3*25+8*7=131
75+56=131
131=131
Hope this helps---ptaylor