document.write( "Question 114217This question is from textbook
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\n" ); document.write( "\n" ); document.write( "The sum of two numbers is 40. The sum of twice the larger and 4 times the smaller is 108. Find the numbers. \n" ); document.write( "
Algebra.Com's Answer #83176 by bucky(2189)\"\" \"About 
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Let L represent the larger number and S represent the smaller number.
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\n" ); document.write( "The problem tells you that the sum of these two numbers equals 40. You can write this in
\n" ); document.write( "equation form as:
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\n" ); document.write( "L + S = 40
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\n" ); document.write( "Next the problem tells you that if you find twice the larger and add it to four times the
\n" ); document.write( "smaller, the sum is 108. Twice the larger is 2L and 4 times the smaller is 4S. Add these two
\n" ); document.write( "products and the result equals 108. In equation form this is:
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\n" ); document.write( "2L + 4S = 108
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\n" ); document.write( "If you go back to the first equation ( L + S = 40 ) and subtract S from both sides you
\n" ); document.write( "get:
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\n" ); document.write( "L = 40 - S
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\n" ); document.write( "Now you can go to the second equation (2L + 4S = 108 ) and substitute 40 - S for L because
\n" ); document.write( "L is equal to 40 - S. When you do that substitution you get:
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\n" ); document.write( "2(40 - S) + 4S = 108
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\n" ); document.write( "Multiply out the left side by taking 2 times each of the terms in the parentheses to
\n" ); document.write( "get:
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\n" ); document.write( "80 - 2S + 4S = 108
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\n" ); document.write( "On the left side combine the -2S and the +4S to get +2S and this makes the equation become:
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\n" ); document.write( "80 + 2S = 108
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\n" ); document.write( "Get rid of the 80 on the left side by subtracting 80 from both sides to reduce the
\n" ); document.write( "equation to:
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\n" ); document.write( "2S = 28
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\n" ); document.write( "Finally, solve for S by dividing both sides by 2 to get:
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\n" ); document.write( "S = 28/2 = 14
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\n" ); document.write( "Now you know that S = 14. But the problem tells you that the sum of L and S equals 40.
\n" ); document.write( "This means that L has to be 26 because 40 - 14 = 26.
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\n" ); document.write( "So the answer to this problem is that the larger number is 26 and the smaller number is 14.
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\n" ); document.write( "Check ... do the two numbers add up to 40? Yes, they do.
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\n" ); document.write( "and does twice the larger (2*26 = 52) and 4 times the smaller (4*14 = 56) add up to be 108?
\n" ); document.write( "Yes, because 52 + 56 = 108.
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\n" ); document.write( "The answer checks.
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\n" ); document.write( "Hope this helps you to see your way through the problem and understand what you can do to
\n" ); document.write( "solve it.
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