The price of eggs rises 10 cents per dozen

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Question from Maddie:

Hi! I'm currently struggling with a word problem that says:
"If the price of eggs rises 10 cents per dozen, one will be able to get 2 dozen fewer eggs with $6.00 than was possible at the lower price. What is the lower price?
We are working on completing the square and all of the problems I've done so far in this chapter require using that method. If possible and needed, could you explain how to set up the equation?

Thank you so much! I appreciate all your help!!

Hi Maddie,

Suppose that the original price is $\$x$ per dozen and at that price you bought $y$ dozen. You paid $\$6$ so you know that

\[x y = 6.\]

Ten cents is $\large \frac{1}{10} \mbox {dollars}\]

so the increased price is $x + \large \frac{1}{10}$ dollars. At this price you buy $y - 2$ dozen for $\$6.$ Hence

\[\left( x + \frac{1}{10} \right) \left( y - 2 \right) = 6.\]

Solve the first equation for $y,$ substitute into the second equation and solve for $x.$

Write back if you need further assistance.

Penny







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