document.write( "Question 497525: Amanda leaves with a basket of hard-boiled eggs to sell. At her first stop she sold half her eggs plus half an egg. At her second stop she sold half her eggs plus half an egg. The same thing occurs at her third, fourth, and fifth stops. When she finishes, she has no eggs in her basket. How many eggs did she start with. Answer is 31. What is the formula to figure out how many eggs? \n" ); document.write( "

Algebra.Com's Answer #336749 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"x%5B0%5D\"$ = the number of eggs she starts with
\n" ); document.write( "After 1st stop, she has
\n" ); document.write( " $\"+x%5B1%5D+=+x%5B0%5D+-+%28x%5B0%5D%2F2+%2B+1%2F2%29+\"$
\n" ); document.write( "After 2nd stop, she has
\n" ); document.write( " $\"+x%5B2%5D+=+x%5B1%5D+-+%28x%5B1%5D%2F2+%2B+1%2F2%29+\"$
\n" ); document.write( "After 3rd stop, she has
\n" ); document.write( " $\"+x%5B3%5D+=+x%5B2%5D+-+%28x%5B2%5D%2F2+%2B+1%2F2%29+\"$
\n" ); document.write( "After 4th stop, she has
\n" ); document.write( " $\"+x%5B4%5D+=+x%5B3%5D+-+%28x%5B3%5D%2F2+%2B+1%2F2%29+\"$
\n" ); document.write( "After 5th stop, she has
\n" ); document.write( " $\"+x%5B5%5D+=+x%5B4%5D+-+%28x%5B4%5D%2F2+%2B+1%2F2%29+\"$
\n" ); document.write( "It is given that $\"+x%5B5%5D+\"$ , the number of eggs
\n" ); document.write( "she ends up with is zero, so
\n" ); document.write( " $\"+x%5B4%5D+-+%28x%5B4%5D%2F2+%2B+1%2F2%29++=+0\"$
\n" ); document.write( " $\"+x%5B4%5D+-+x%5B4%5D%2F2+-+1%2F2+=+0+\"$
\n" ); document.write( " $\"+x%5B4%5D%2F2+=+1%2F2+\"$
\n" ); document.write( " $\"+x%5B4%5D+=+1+\"$
\n" ); document.write( "So, after the 4th stop,
\n" ); document.write( " $\"+x%5B3%5D+-+%28x%5B3%5D%2F2+%2B+1%2F2%29+=+1\"$
\n" ); document.write( " $\"+x%5B3%5D%2F2+-+1%2F2+=+1+\"$
\n" ); document.write( " $\"+x%5B3%5D%2F2+=+3%2F2+\"$
\n" ); document.write( " $\"+x%5B3%5D+=+3+\"$
\n" ); document.write( "After the 3rd stop,
\n" ); document.write( " $\"+x%5B2%5D+-+%28x%5B2%5D%2F2+%2B+1%2F2%29+=+3\"$
\n" ); document.write( " $\"+x%5B2%5D%2F2+-+1%2F2+=+3+\"$
\n" ); document.write( " $\"+x%5B2%5D%2F2+=+7%2F2+\"$
\n" ); document.write( " $\"+x%5B2%5D+=+7+\"$
\n" ); document.write( "After the 2nd stop,
\n" ); document.write( " $\"++x%5B1%5D+-+%28x%5B1%5D%2F2+%2B+1%2F2%29+=+7+\"$
\n" ); document.write( " $\"+x%5B1%5D%2F2+-+1%2F2+=+7+\"$
\n" ); document.write( " $\"+x%5B1%5D%2F2+=+15%2F2+\"$
\n" ); document.write( " $\"+x%5B1%5D+=+15+\"$
\n" ); document.write( "After the 1st stop,
\n" ); document.write( " $\"+x%5B0%5D+-+%28x%5B0%5D%2F2+%2B+1%2F2%29+=+15+\"$
\n" ); document.write( " $\"+x%5B0%5D+%2F2+-+1%2F2+=+15+\"$
\n" ); document.write( " $\"+x%5B0%5D%2F2+=+31%2F2+\"$
\n" ); document.write( " $\"+x%5B0%5D+=+31+\"$
\n" ); document.write( "She started with 31 eggs
\n" ); document.write( "check answer:
\n" ); document.write( "31 - ( 15.5 + .5 ) = 31 - 16
\n" ); document.write( "31 - 16 = 15
\n" ); document.write( "------------
\n" ); document.write( "15 - ( 7.5 + .5 ) = 15 - 8
\n" ); document.write( "15 - 8 = 7
\n" ); document.write( "---------
\n" ); document.write( "7 - (3.5 + .5) = 7 - 4
\n" ); document.write( "7 - 4 = 3
\n" ); document.write( "----------
\n" ); document.write( "3 - (1.5 + .5) = 3 - 2
\n" ); document.write( "3 - 2 = 1
\n" ); document.write( "---------
\n" ); document.write( "1 - (.5 + .5) = 1 - 1
\n" ); document.write( "1 - 1 = 0
\n" ); document.write( "---------
\n" ); document.write( "OK \n" ); document.write( "

\n" );