document.write( "Question 412103: There are four numbers. The first is 20 less than the second, the thrid is one more than twice the first. The fourth is 4 morethan the second. I also know tat the sum of the first and second equals the third and fourth numbers. Find the numbers. \r
\n" ); document.write( "\n" ); document.write( " Thanks for helping =) \n" ); document.write( "

Algebra.Com's Answer #289530 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
there are 4 unknowns, so I need to somehow get
\n" ); document.write( "4 equations in order to solve.
\n" ); document.write( "call the numbers a,b,c, and d
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"a+=+b+-+20\"$
\n" ); document.write( "(2) $\"c+=+2a+%2B+1\"$
\n" ); document.write( "(3) $\"d+=+b+%2B+4\"$
\n" ); document.write( "(4) $\"a+%2B+b+=+c+%2B+d\"$
\n" ); document.write( "OK, I have 4 equations, so it's solvable.
\n" ); document.write( "----------------
\n" ); document.write( "Substitute (1) and (3) in (4)
\n" ); document.write( "(4) $\"a+%2B+b+=+c+%2B+d\"$
\n" ); document.write( "(4) $\"b+-+20+%2B+b+=+c+%2B+b+%2B+4\"$
\n" ); document.write( "(4) $\"2b+-+20+=+c+%2B+b+%2B+4\"$
\n" ); document.write( "(4) $\"c+=+b+-+24\"$
\n" ); document.write( "--------------
\n" ); document.write( "Substitute (1) in (2)
\n" ); document.write( "(2) $\"c+=+2%2A%28b+-+20%29+%2B+1\"$
\n" ); document.write( "(2) $\"c+=+2b+-+40+%2B+1\"$
\n" ); document.write( "(2) $\"c+=+2b+-+39\"$
\n" ); document.write( "----------------
\n" ); document.write( "Substitute this value of $\"c\"$ in (4)
\n" ); document.write( "(4) $\"c+=+b+-+24\"$
\n" ); document.write( "(4) $\"2b+-+39+=+b+-+24\"$
\n" ); document.write( "(4) $\"b+=+15\"$
\n" ); document.write( "----------------
\n" ); document.write( "Plug this into (1)
\n" ); document.write( "(1) $\"a+=+b+-+20\"$
\n" ); document.write( "(1) $\"a+=+15+-+20\"$
\n" ); document.write( "(1) $\"a+=+-5\"$
\n" ); document.write( "----------------
\n" ); document.write( "Plug this into (2)
\n" ); document.write( "(2) $\"c+=+2a+%2B+1\"$
\n" ); document.write( "(2) $\"c+=+2%2A%28-5%29+%2B+1\"$
\n" ); document.write( "(2) $\"c+=+-9\"$
\n" ); document.write( "----------------
\n" ); document.write( "Plug $\"b+=+15\"$ into (3)
\n" ); document.write( "(3) $\"d+=+b+%2B+4\"$
\n" ); document.write( "(3) $\"d+=+15+%2B+4\"$
\n" ); document.write( "(3) $\"d+=+19\"$
\n" ); document.write( "-----------------
\n" ); document.write( "The numbers are:
\n" ); document.write( "-5, 15, -9, and 19
\n" ); document.write( "check answer:
\n" ); document.write( "(1) $\"a+=+b+-+20\"$
\n" ); document.write( " $\"-5+=+15+-+20\"$
\n" ); document.write( " $\"-5+=+-5\"$
\n" ); document.write( "OK
\n" ); document.write( "(2) $\"c+=+2a+%2B+1\"$
\n" ); document.write( " $\"-9+=+2%2A%28-5%29+%2B+1\"$
\n" ); document.write( " $\"-9+=+-10+%2B+1\"$
\n" ); document.write( " $\"-9+=+-9\"$
\n" ); document.write( "OK
\n" ); document.write( "(3) $\"d+=+b+%2B+4\"$
\n" ); document.write( " $\"19+=+15+%2B+4\"$
\n" ); document.write( " $\"19+=+19\"$
\n" ); document.write( "OK
\n" ); document.write( "(4) $\"a+%2B+b+=+c+%2B+d\"$
\n" ); document.write( " $\"-5+%2B+15+=+-9+%2B+19\"$
\n" ); document.write( " $\"10+=+10\"$
\n" ); document.write( "OK \n" ); document.write( "

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