Question

A store gets a bucket of eggs for $16.20 and sells a dozen eggs for $3.50. If there are 450 eggs in the bucket, by what percent has the store increased the price per dozen eggs?

Answer 1

Price of a bucket of eggs $16.20
price for a dozen of eggs $3.50
number of dozens in 450 eggs:
450/12
=37.5
price of 37.5 will be:
37.5×3.50=$131.25
The percentage the store has increased the price will be:
(131.25-16.20)/16.20×100
=710%

Answer 2

The store increased the price of eggs per dozen by $\boxed{710 .185\:\%}$.

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 $100$.  

The cost of the total eggs in the bucket is $\ \:16.2$ and there are $450$ eggs in the bucket.

A dozen is a grouping of twelve(in this case grouping of twelve eggs).

Here, $12$ eggs make up 1 dozen which implies 1 egg make up $\frac{1}{12}$ of a dozen. Therefore, $450$ eggs make up $450\cdot\dfrac{1}{12}$ of a dozen.

$\boxed{\begin{aligned}\text{Dozen of eggs in the bucket}&=450\cdot\frac{1}{12}\\&= 37.5 \text{ dozens}\end{aligned}}$

Therefore, the bucket consists of $37.5$ dozens of eggs.

The store gets a bucket of eggs for $\ \:16.20$ and one bucket has $37.5$ dozen of eggs then the store gets a dozen eggs at a price calculated as shown below.

$\boxed{\begin{aligned}\text{Cost price of a dozen of eggs}&=\frac{ (\ \:16.20)}{37.50}\\ &=\ \:0.432\end{aligned}}$

The store is selling the eggs at $\ \:3.50$ per dozen. So , the increased amount is calculated as the difference in the selling price and the cost price.

$\boxed{\begin{aligned}\text{Increased price}&= 3.50 - 0.432\\&=\ \:3.068\end{aligned}}$

The percent by which the store increased the price per dozen of eggs is calculated as shown below.

$\boxed{\begin{aligned}\text{Percentage increase in price}&= \frac{3.068}{0.432}\cdot100\\&= 710.185\:\%\end{aligned}}$

The percentage increase in the price of eggs per dozen is $\boxed{710 .185\:\%}$.

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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.