document.write( "Question 93172: A bill of $123 was paid with $5 and $1 coins, a total of 59 notes being used. how many $5 notes were used? \n" ); document.write( "
Algebra.Com's Answer #67809 by bucky(2189)\"\" \"About 
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Let F represent the number of $5 notes and let S represent the number of $1 notes.
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\n" ); document.write( "Since the total number of notes used is 59, you can write an equation for the total as:
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\n" ); document.write( "F + S = 59 <==== equation 1
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\n" ); document.write( "Since the total monetary value of the $5 notes is $5 times F and the total monetary
\n" ); document.write( "value of the $1 notes is $1 times S you can add these two monetary values and set the sum
\n" ); document.write( "equal to the $123 bill. In equation form this is:
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\n" ); document.write( "5*F + 1*S = 123 <====equation 2
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\n" ); document.write( "These two equations can be solved as a set. One way to do this is to go to equation 1
\n" ); document.write( "and solve it for one variable in terms of the other. For example, if you subtract F
\n" ); document.write( "from both sides of equation 1 the result is:
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\n" ); document.write( "S = 59 - F
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\n" ); document.write( "Next you can use that result to modify equation 2. Since S and 59 - F are equal, in equation 2
\n" ); document.write( "you can replace S with the quantity (59 - F). When you do that equation 2 becomes:
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\n" ); document.write( "5*F + 1*(59 - F) = 123
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\n" ); document.write( "This simplifies to:
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\n" ); document.write( "5F + 59 - F = 123
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\n" ); document.write( "On the left side, you can combine the 5F and -F to get 4F. This simplifies the equation into:
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\n" ); document.write( "4F + 59 = 123
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\n" ); document.write( "Next you can get rid of the 59 on the left side by subtracting 59 from both sides of the
\n" ); document.write( "equation. This results in:
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\n" ); document.write( "4F = 64
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\n" ); document.write( "Finally you can solve for F by dividing both sides by 4 to get:
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\n" ); document.write( "F = 64/4 = 16
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\n" ); document.write( "Since F represents the number of $5 notes, you now know there are 15 $5 notes.
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\n" ); document.write( "If there are 16 each of the $5 notes and the total number of notes is 59, that means that
\n" ); document.write( "there must be 59 - 16 or 43 each of the $1 notes.
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\n" ); document.write( "You can check that out to make sure the result is enough to pay the $123 bill. If you count
\n" ); document.write( "out 16 of the $5 notes you get $80 ... 16 times $5 = $80. Then you add to that amount
\n" ); document.write( "43 of the $1 notes and the total is $80 + $43 = $123. That works! So your answer is correct
\n" ); document.write( "and the answer to the problem is that there are 16 of the $5 notes used in paying the
\n" ); document.write( "bill.
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\n" ); document.write( "Hope this helps you to understand the problem.
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