Question 965860
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The language use in the statement of the problem is definitely poor, leaving the problem open to different interpretations.  With one interpretation of the problem, you could pay the $75 with 15 $5 bills and still have 12 bills (of either $1 or $5 denominations) left.<br>
Assuming the intent of the problem is to use exactly all 27 bills to make the payment, the solution by the other tutor is a good typical algebraic solution.<br>
You can get good mental exercise by solving a problem like this using logical reasoning and simple mental arithmetic, perhaps like this:<br>
The total to be paid is $75; since any number of $5 bills makes a total that is a multiple of $5, the total value of the $1 bills must also be a multiple of 5.  So the number of $1 bills is either 5, 10, 15, 20, or 25.<br>
Then a few quick mental calculations show the correct total is with 15 $1 bills: 15($1)+12($5) = $15+$60 = $75<br>