SOLUTION: A cashier has a total of 126 bills, made up of fives and tens. The total value of the money is $840. How many of each kind of bill does he have?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A cashier has a total of 126 bills, made up of fives and tens. The total value of the money is $840. How many of each kind of bill does he have?      Log On


   

Question 214937: A cashier has a total of 126 bills, made up of fives and tens. The total value of the money is $840. How many of each kind of bill does he have?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
A cashier has a total of 126 bills, made up of fives and tens. The total value of the money is $840. How many of each kind of bill does he have?

Step 1. Let x be t;he number of fives and let 126-x be the number of tens.

Step 2. Let 5x be the total value consisting of fives

Step 3. Let 10(126-x) be the total value consisting of tens.

Step 4. 5x+10(126-x)=840 Add Steps 2 and 3 to get $840.

Step 5. The following 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=84.
  • Graphical form: Equation 5x%2B10%2A%28126-x%29=840 was fully solved.
  • Text form: 5x+10*(126-x)=840 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+5x%2B10%2A%28126-x%29=840+%29
    For tutors: simplify_cartoon( 5x+10*(126-x)=840 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 5%2Ax%2B10%2A%28highlight_red%28+126+%29-x%29=840.
Moved 126 to the right of expression
It becomes 5%2Ax%2B10%2A%28-x%2Bhighlight_green%28+126+%29%29=840.
Look at 5%2Ax%2B10%2A%28-x%2B126%29=highlight_red%28+840+%29.
Moved these terms to the left highlight_green%28+-840+%29
It becomes 5%2Ax%2B10%2A%28-x%2B126%29-highlight_green%28+840+%29=0.
Look at 5%2Ax%2Bhighlight_red%28+10%2A%28-x%2B126%29+%29-840=0.
Expanded term 10 by using associative property on %28-x%2B126%29
It becomes 5%2Ax-highlight_green%28+10%2Ax+%29%2Bhighlight_green%28+10%2A126+%29-840=0.
Look at 5%2Ax-10%2Ax%2Bhighlight_red%28+10+%29%2Ahighlight_red%28+126+%29-840=0.
Multiplied numerator integers
It becomes 5%2Ax-10%2Ax%2Bhighlight_green%28+1260+%29-840=0.
Look at 5%2Ax-10%2Ax%2Bhighlight_red%28+1260+%29-highlight_red%28+840+%29=0.
Added fractions or integers together
It becomes 5%2Ax-10%2Ax%2Bhighlight_green%28+420+%29=0.
Look at highlight_red%28+5%2Ax+%29-highlight_red%28+10%2Ax+%29%2B420=0.
Eliminated similar terms highlight_red%28+5%2Ax+%29,highlight_red%28+-10%2Ax+%29 replacing them with highlight_green%28+%285-10%29%2Ax+%29
It becomes highlight_green%28+%285-10%29%2Ax+%29%2B420=0.
Look at %28highlight_red%28+5+%29-highlight_red%28+10+%29%29%2Ax%2B420=0.
Added fractions or integers together
It becomes %28highlight_green%28+-5+%29%29%2Ax%2B420=0.
Look at %28highlight_red%28+-5+%29%29%2Ax%2B420=0.
Removed extra sign in front of -5
It becomes %28-highlight_green%28+5+%29%29%2Ax%2B420=0.
Look at highlight_red%28+%28-highlight_red%28+5+%29%29%2Ax+%29%2B420=0.
Remove unneeded parentheses around factor highlight_red%28+5+%29
It becomes -highlight_green%28+5+%29%2Ax%2B420=0.
Look at highlight_red%28+-5%2Ax%2B420+%29=0.
Solved linear equation highlight_red%28+-5%2Ax%2B420=0+%29 equivalent to -5*x+420 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=84.

Universal Simplifier and Solver


Done!



With x=84 then 126-x=42

Step 6. The number of fives is 84 and the number of tens is 42

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J