document.write( "Question 924988: The sum of two numbers is 103. If four times the smaller number is subtracted from the larger number, the result is 8. Find the two numbers. \n" ); document.write( "
Algebra.Com's Answer #561246 by DrBeeee(684)\"\" \"About 
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Let L = the larger number and
\n" ); document.write( "Let s = the smaller number
\n" ); document.write( "From the problem statement we have
\n" ); document.write( "(1) s + L = 103 and
\n" ); document.write( "(2) L - 4*s = 8
\n" ); document.write( "You need, and have, two equations to solve for two unknowns (the two numbers).
\n" ); document.write( "You can use any of the techniques you learned to solve simultaneous equations. Let's use substitution. Solve (2) for L and get
\n" ); document.write( "(3) L = 8 + 4*s
\n" ); document.write( "Now put L of (3) into (1) and get
\n" ); document.write( "(4) s + 8 + 4*s = 103 or
\n" ); document.write( "(5) 5*s = 103 - 8 or
\n" ); document.write( "(6) 5*s = 95 or
\n" ); document.write( "(7) s = 95/5 or
\n" ); document.write( "(8) s = 19
\n" ); document.write( "Now put s of (8) into (2) to get
\n" ); document.write( "(9) L - 4*19 = 8 or
\n" ); document.write( "(10) L = 8 + 4*19 or
\n" ); document.write( "(11) L = 8 + 76 or
\n" ); document.write( "(12) L = 84
\n" ); document.write( "Now use (2) to check your answer.
\n" ); document.write( "Is (L - 4*S = 8)?
\n" ); document.write( "Is (84 - 4*19 = 8)?
\n" ); document.write( "Is (84 -76 = 8)?
\n" ); document.write( "Is (8 = 8)? Yes
\n" ); document.write( "Answer: The smaller number is 19 and the larger number is 84.
\n" ); document.write( "REM: you need to write two independent equations to solve for two unknowns. If you have three unknowns, like in many coin problems, you need three independent equations, etc. etc.\r
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