document.write( "Question 889122: The average Of four numbers is 56. The first number is 5 more than the second ; the third number is half of the second and the fourth number is three times the sum of the first and second numbers. Find the numbers.? \n" ); document.write( "

Algebra.Com's Answer #537907 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ , $\"+b+\"$ , $\"+c+\"$ , and $\"+d+\"$ be the numbers
\n" ); document.write( "(1) $\"+%28+a+%2B+b+%2B+c+%2B+d+%29+%2F+4+=+56+\"$
\n" ); document.write( "(2) $\"+a+=+b+%2B+5+\"$
\n" ); document.write( "(3) $\"+c+=+%281%2F2%29%2Ab+\"$
\n" ); document.write( "(4) $\"+d+=+3%2A%28+a+%2B+b+%29+\"$
\n" ); document.write( "----------------------
\n" ); document.write( "Substitute (2) into (4)
\n" ); document.write( "(4) $\"+d+=+3%2A%28+b+%2B+5+%2B+b+%29+\"$
\n" ); document.write( "(4) $\"+d+=+3%2A%28+2b+%2B+5+%29+\"$
\n" ); document.write( "(4) $\"+d+=+6b+%2B+15+\"$
\n" ); document.write( "-----------------------
\n" ); document.write( "Substitute (2), (3), and (4) into (1)
\n" ); document.write( "(1) $\"+%28+a+%2B+b+%2B+c+%2B+d+%29+%2F+4+=+56+\"$
\n" ); document.write( "(1) $\"+%28+b+%2B+5+%2B+b+%2B+%281%2F2%29%2Ab+%2B+6b+%2B+15+%29+%2F+4+=+56+\"$
\n" ); document.write( "(1) $\"+%28+%28+17%2F2+%29%2Ab+%2B+20+%29+%2F+4+=+56+\"$
\n" ); document.write( "Multiply both sides by $\"+4+\"$
\n" ); document.write( "(1) $\"++%28+17%2F2+%29%2Ab+%2B+20++=+224+\"$
\n" ); document.write( "Multiply both sides by $\"+2+\"$
\n" ); document.write( "(1) $\"+17b+%2B+40+=+448+\"$
\n" ); document.write( "(1) $\"+17b+=+408+\"$
\n" ); document.write( "(1) $\"+b+=+24+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+a+=+b+%2B+5+\"$
\n" ); document.write( "(2) $\"+a+=+24+%2B+5+\"$
\n" ); document.write( "(2) $\"+a+=+29+\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"+c+=+%281%2F2%29%2A24+\"$
\n" ); document.write( "(3) $\"+c+=+12+\"$
\n" ); document.write( "and
\n" ); document.write( "(4) $\"+d+=+6%2A24+%2B+15+\"$
\n" ); document.write( "(4) $\"+d+=+144+%2B+15+\"$
\n" ); document.write( "(4) $\"+d+=+159+\"$
\n" ); document.write( "-------------------
\n" ); document.write( "The numbers are 29, 24, 12, and 159
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+%28+a+%2B+b+%2B+c+%2B+d+%29+%2F+4+=+56+\"$
\n" ); document.write( "(1) $\"+%28+29+%2B+24+%2B+12+%2B+159+%29+%2F+4+=+56+\"$
\n" ); document.write( "(1) $\"+224%2F4+=+56+\"$
\n" ); document.write( "(1) $\"+224+=+224+\"$
\n" ); document.write( "OK\r
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