Question 1128574



Let {{{L}}} be the lower price per dozen of eggs, in dollars (which is under the question).

Then the new price is {{{(L+0.1) }}}dollars per dozen.      (Notice {{{0.1 dollars = 10 cents}}})


At the lower price, the buyer could buy {{{6/L}}} dozens for {{{6 }}}dollars.


At the new price, it can buy only {{{6/(L+0.1)}}} dozens.


The condition says that this difference is {{{2}}} dozens:

{{{6/L - 6/(L+0.1)= 2}}}


To solve this equation, multiply both sides by{{{ L*(L+0.1)}}}. You will get

{{{6*(L+0.1) - 6L = 2*L*(L+0.1)}}}


Simplify it step by step:

{{{6L + 0.6 - 6L = 2L^2 + 0.2L}}},

{{{0.6 = 2L^2 + 0.2L}}}  

{{{2L^2 + 0.2L - 0.6 = 0}}}  .............. divide by {{{2}}} both sides  

{{{L^2 + 0.1L  = 0.3}}}............complete square: 

{{{(L^2 + 0.1L+b^2)-b^2  = 0.3}}}

coefficient {{{a=1}}}, {{{2ab=0.1}}}=>{{{2*1b=0.1}}}=>{{{b=0.1/2}}}->{{{b=0.05}}}


{{{(L^2 + 0.1L+0.05^2)-0.05^2  = 0.3}}}

{{{(L +0.05)^2-0.0025  = 0.3}}}

{{{(L +0.05)^2 = 0.3+0.0025 }}}

{{{(L +0.05)^2 = 0.3025 }}}

{{{L +0.05 =sqrt( 0.3025) }}}

{{{L  = (-0.05+-sqrt( 0.3025)) }}}

{{{L  = (-0.05+-0.55) }}}


so, roots are:

{{{L}}}≈{{{-0.6}}}

{{{L}}}≈{{{0.5}}} -> we need only positive root because price cannot be negative number


Answer.  The lower price was ${{{0.5}}} per dozen of eggs.


Check:   
{{{6/0.5 = 12}}}   
{{{6/(0.5+0.1) = 6/0.6 = 10}}}
{{{   12 - 10 = 2}}}   ! Correct !