document.write( "Question 918962: The price of milk is increased by 20%.Find by how much percent a housewife should reduce the consumption of milk so as to not to increase her expenditure? \n" ); document.write( "

Algebra.Com's Answer #557340 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+p+\"$ = price per unit before going up
\n" ); document.write( " $\"+p+%2B+.2p+=+1.2p+\"$ = price per unit after going up
\n" ); document.write( "I can say they consumed any amount before
\n" ); document.write( "the price rose. I will say they consumed
\n" ); document.write( " $\"+100+\"$ units ( any units )
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\n" ); document.write( "Let $\"+k+\"$ = the fraction to reduce consumption by
\n" ); document.write( " $\"+100p+=+%28+100+-+100k+%29%2A1.2p+\"$
\n" ); document.write( " $\"+100p+=+100%2A%28+1+-+k+%29%2A1.2p+\"$
\n" ); document.write( "Divide both sides by $\"+100p+\"$
\n" ); document.write( " $\"+1+=+1.2%2A%28+1+-+k+%29+\"$
\n" ); document.write( " $\"+1+=+1.2+-+1.2k+\"$
\n" ); document.write( " $\"+1.2k+=+.2+\"$
\n" ); document.write( " $\"+k+=+1%2F6+\"$
\n" ); document.write( "She needs to reduce consumption by 16.67%
\n" ); document.write( "check:
\n" ); document.write( "Say $\"+p+=+7+\"$
\n" ); document.write( " $\"+p+%2B+.2p+=+1.2%2A7+\"$
\n" ); document.write( " $\"+1.2%2A7+=+8.4+\"$
\n" ); document.write( "----------------
\n" ); document.write( "Say they consume $\"+11+\"$ units
\n" ); document.write( " $\"+11%2A7+=+77+\"$ is the cost of milk before increase
\n" ); document.write( "-------------
\n" ); document.write( "Then they consume $\"+11+-+%281%2F6%29%2A11+=+55%2F6+\"$ units
\n" ); document.write( "after increase
\n" ); document.write( " $\"+8.4%2A%2855%2F6%29+=+77+\"$
\n" ); document.write( "Their cost still is the same after increase in price -OK\r
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