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\n" ); document.write( "(1) The fastest way to the answer: trial and error with simple mental arithmetic.
\n" ); document.write( "Find pairs of integers b and c for which the product bc is 60, then find the pair for which 3b+c=41. Answer b=12, c=5.
\n" ); document.write( "Then use 2a+3b=52 with b=12 to find a=8.
\n" ); document.write( "And last a+b+c = 8+12+5 = 25.
\n" ); document.write( "ANSWER: 25
\n" ); document.write( "(2) Using formal algebra....
\n" ); document.write( "3b+c=41
\n" ); document.write( "c = 41-3b
\n" ); document.write( "bc = b(41-3b) = 60
\n" ); document.write( "41b-3b^2 = 60
\n" ); document.write( "3b^2-41b+60 = 0
\n" ); document.write( "Factor into the form
\n" ); document.write( "(3b-m)(b-n) = 0
\n" ); document.write( "3b^2-(m+3n)+mn=0
\n" ); document.write( "We need mn=60 and m+3n=41....
\n" ); document.write( "Note that is exactly what we needed in solving the problem using trial and error -- so using the formal algebra didn't make solving the problem easier.
\n" ); document.write( "However, assuming this question comes from a formal math course, you should know how to set up and solve the problem using the formal algebra.
\n" ); document.write( "Continuing then...
\n" ); document.write( "(3b-5)(b-12)=0
\n" ); document.write( "b = 5/3 (not an integer) or b=12; so b=12
\n" ); document.write( "Then, as before, c=5 and a=8.
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