Question 1101202
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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 = 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 = 0

{{{L{1,2]}}} = {{{(-0.1 +- sqrt(0.1^2 + 4*0.3))/2}}} = {{{(-0.1 +- 1.1)/2}}}.


The only positive root is  L = {{{(-0.1 + 1.1)/2}}} = 0.5.


<U>Answer</U>.  The lower price was $0.5 per dozen of eggs.


<U>Check</U>.   {{{6/0.5}}} = 12;   {{{6/(0.5+0.1)}}} = {{{6/0.6}}} = 10;   12 - 10 = 2   ! Correct !
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Solved.