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You can put this solution on YOUR website!
\n" ); document.write( "You have received three responses showing -- or at least describing -- formal algebraic solutions.
\n" ); document.write( "I have a comment regarding those responses.
\n" ); document.write( "Look at the sentence that says \"The total value of the $2 notes is $94 less than the total value of the $10 notes\".
\n" ); document.write( "Tutor @josgarithmetic says that translates to the equation
\n" ); document.write( "Tutor @math_tutor2020 says it translates to
\n" ); document.write( "Although the two equations are equivalent, the second one is FAR better. The first one can teach a student to interpret worded information incorrectly, while the second teaches it correctly. \"$94 less than (expression)\" means you start with the (expression) and subtract 94. You don't start with the \"-94\" and add the (expression).
\n" ); document.write( "While you should understand how to solve the problem using formal algebra (and even though a formal solution was probably required), you should understand that being able to solve the problem informally using logical reasoning and simple arithmetic gives you valuable problem-solving exercise.
\n" ); document.write( "In this problem, you can loan Bob 3 more $2 notes to make the number of $10 and $2 notes equal; the total value of the $2 notes is then only $94-$6 = $88 less than the value of the $10 notes. And since the value of each $2 note is $8 less than the value of each $10 note, the number of notes of each kind he has must be $88/$8 = 11.
\n" ); document.write( "Then have Bob give you back the 3 $2 notes you loaned him, leaving him with....
\n" ); document.write( "ANSWER: 11-3 = 8 $2 notes (and 11 $10 notes)
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