SOLUTION: Thirty students bought pennants for the football game. Plain pennants cost $4 each and fancy ones cost $8 each. If the total bill was $168, how many students bought the fancy pen

Algebra ->  Equations -> SOLUTION: Thirty students bought pennants for the football game. Plain pennants cost $4 each and fancy ones cost $8 each. If the total bill was $168, how many students bought the fancy pen      Log On


   

Question 215856: Thirty students bought pennants for the football game. Plain pennants cost $4 each and fancy ones cost $8 each. If the total bill was $168, how many students bought the fancy pennants?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Thirty students bought pennants for the football game. Plain pennants cost $4 each and fancy ones cost $8 each. If the total bill was $168, how many students bought the fancy pennants?

Step 1. Let x be the number of fancy pennants bought by students.

Step 2. Let 30-x be the number of plain pennants bought by students.

Step 3. Let 8x be the dollar value of the fancy pennants bought by students.

Step 4. Let 4(30-x) be the dollar value of the fancy pennants bought by students.

Step 5. Total cost is then 8x%2B4%2830-x%29=168 as given by the problem statement. The following steps will solve this equation:

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


YOUR ANSWER


  • This is an equation! Solutions: x=12.
  • Graphical form: Equation 8x%2B4%2A%2830-x%29=168 was fully solved.
  • Text form: 8x+4*(30-x)=168 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+8x%2B4%2A%2830-x%29=168+%29
    For tutors: simplify_cartoon( 8x+4*(30-x)=168 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 8%2Ax%2B4%2A%28highlight_red%28+30+%29-x%29=168.
Moved 30 to the right of expression
It becomes 8%2Ax%2B4%2A%28-x%2Bhighlight_green%28+30+%29%29=168.
Look at 8%2Ax%2B4%2A%28-x%2B30%29=highlight_red%28+168+%29.
Moved these terms to the left highlight_green%28+-168+%29
It becomes 8%2Ax%2B4%2A%28-x%2B30%29-highlight_green%28+168+%29=0.
Look at 8%2Ax%2Bhighlight_red%28+4%2A%28-x%2B30%29+%29-168=0.
Expanded term 4 by using associative property on %28-x%2B30%29
It becomes 8%2Ax-highlight_green%28+4%2Ax+%29%2Bhighlight_green%28+4%2A30+%29-168=0.
Look at 8%2Ax-4%2Ax%2Bhighlight_red%28+4+%29%2Ahighlight_red%28+30+%29-168=0.
Multiplied numerator integers
It becomes 8%2Ax-4%2Ax%2Bhighlight_green%28+120+%29-168=0.
Look at 8%2Ax-4%2Ax%2Bhighlight_red%28+120+%29-highlight_red%28+168+%29=0.
Added fractions or integers together
It becomes 8%2Ax-4%2Ax%2Bhighlight_green%28+-48+%29=0.
Look at 8%2Ax-4%2Ax%2Bhighlight_red%28+-48+%29=0.
Removed extra sign in front of -48
It becomes 8%2Ax-4%2Ax-highlight_green%28+48+%29=0.
Look at highlight_red%28+8%2Ax+%29-highlight_red%28+4%2Ax+%29-48=0.
Eliminated similar terms highlight_red%28+8%2Ax+%29,highlight_red%28+-4%2Ax+%29 replacing them with highlight_green%28+%288-4%29%2Ax+%29
It becomes highlight_green%28+%288-4%29%2Ax+%29-48=0.
Look at %28highlight_red%28+8+%29-highlight_red%28+4+%29%29%2Ax-48=0.
Added fractions or integers together
It becomes %28highlight_green%28+4+%29%29%2Ax-48=0.
Look at highlight_red%28+%28highlight_red%28+4+%29%29%2Ax+%29-48=0.
Remove unneeded parentheses around factor highlight_red%28+4+%29
It becomes highlight_green%28+4+%29%2Ax-48=0.
Look at highlight_red%28+4%2Ax-48+%29=0.
Solved linear equation highlight_red%28+4%2Ax-48=0+%29 equivalent to 4*x-48 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=12.

Universal Simplifier and Solver


Done!



With x=12, then 30-x=18

Check total cost if true...8*12+4*18=96+72=168...which is a true statement

Step 6. ANSWER: 12 students bought the fancy pennants.

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