The store increased the price of eggs per dozen by [tex]\boxed{710 .185\:\%}[/tex].
Explanation:
The percentage (symbolized by %) is described as a portion of a quantity expressed as a number with respect to total quantity where the total quantity is taken to be [tex]100[/tex].
The cost of the total eggs in the bucket is [tex]\$\:16.2[/tex] and there are [tex]450[/tex] eggs in the bucket.
A dozen is a grouping of twelve(in this case grouping of twelve eggs).
Here, [tex]12[/tex] eggs make up 1 dozen which implies 1 egg make up [tex]\frac{1}{12}[/tex] of a dozen. Therefore, [tex]450[/tex] eggs make up [tex]450\cdot\dfrac{1}{12}[/tex] of a dozen.
[tex]\boxed{\begin{aligned}\text{Dozen of eggs in the bucket}&=450\cdot\frac{1}{12}\\&= 37.5 \text{ dozens}\end{aligned}}[/tex]
Therefore, the bucket consists of [tex]37.5[/tex] dozens of eggs.
The store gets a bucket of eggs for [tex]\$\:16.20[/tex] and one bucket has [tex]37.5[/tex] dozen of eggs then the store gets a dozen eggs at a price calculated as shown below.
[tex]\boxed{\begin{aligned}\text{Cost price of a dozen of eggs}&=\frac{ (\$\:16.20)}{37.50}\\ &=\$\:0.432\end{aligned}}[/tex]
The store is selling the eggs at [tex]\$\:3.50[/tex] per dozen. So , the increased amount is calculated as the difference in the selling price and the cost price.
[tex]\boxed{\begin{aligned}\text{Increased price}&= 3.50 - 0.432\\&=\$\:3.068\end{aligned}}[/tex]
The percent by which the store increased the price per dozen of eggs is calculated as shown below.
[tex]\boxed{\begin{aligned}\text{Percentage increase in price}&= \frac{3.068}{0.432}\cdot100\\&= 710.185\:\%\end{aligned}}[/tex]
The percentage increase in the price of eggs per dozen is [tex]\boxed{710 .185\:\%}[/tex].
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Answer Details:
Grade: Middle School
Subject: Mathematics
Chapter: Percentage
Keywords: Percentage, cost price, selling price, profit, loss, increase, decrease, store, bucket, dozen, eggs.
