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

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) (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 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 was fully solved.
Text form: 8x+4*(30-x)=168 simplifies to 0=0
Cartoon (animation) form:
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 .
Moved

to the right of expression
It becomes .

Look at .
Moved these terms to the left highlight_green%28+-168+%29

It becomes .

Look at .
Expanded term

by using associative property on %28-x%2B30%29

It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
Added fractions or integers together
It becomes .

Look at .
Removed extra sign in front of

It becomes .

Look at .
Eliminated similar terms highlight_red%28+8%2Ax+%29

replacing them with highlight_green%28+%288-4%29%2Ax+%29

It becomes .

Look at .
Added fractions or integers together
It becomes .

Look at .
Remove unneeded parentheses around factor highlight_red%28+4+%29

It becomes .

Look at .
Solved linear equation highlight_red%28+4%2Ax-48=0+%29

equivalent to 4*x-48 =0
It becomes .
Result:
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
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