Leann's Bakery Pie Sale Solve The Math And Find The Total Earnings

Hey there, math enthusiasts and pie lovers! Let's dive into a delicious problem from Leann's Bakery. They recently held a pie sale, and it sounds like it was quite a hit! All pies were sold for a sweet $5.00 each. Now, here's where it gets interesting: two out of every three pies sold were cheese pies, one out of every five pies was chicken, and the rest were beef. The real kicker? Leann's Bakery sold 24 more cheese pies than beef pies. Our mission, should we choose to accept it, is to figure out the total money collected from this pie extravaganza. So, grab a slice of your favorite pie (metaphorically, of course!) and let's get started!

Breaking Down the Pie Proportions

To crack this math problem, we need to dissect the proportions of pies sold. First off, we know that cheese pies made up two-thirds (2/3) of the total pies sold, which is a significant chunk of the pie chart, literally! Next up, chicken pies accounted for one-fifth (1/5) of the total. That leaves us with beef pies, which represent the remaining portion. To figure out what fraction of the total beef pies represent, we need to do a little fraction arithmetic. Think of the total number of pies as a whole, which we can represent as 1. To find the fraction of beef pies, we subtract the fractions of cheese and chicken pies from 1. So, the equation looks like this: 1 - (2/3) - (1/5).

Before we can subtract these fractions, we need to find a common denominator. The least common denominator for 3 and 5 is 15. So, we convert the fractions: 2/3 becomes 10/15, and 1/5 becomes 3/15. Now our equation looks like this: 1 - (10/15) - (3/15). We can also express 1 as 15/15. So, the equation transforms to: (15/15) - (10/15) - (3/15). Doing the subtraction, we get (15 - 10 - 3)/15 = 2/15. Therefore, beef pies made up 2/15 of the total pies sold. This fraction calculation is a fundamental step in solving the problem, laying the groundwork for determining the actual number of each pie type sold.

The Cheese and Beef Pie Difference

Now, let's zoom in on the critical piece of information: Leann's Bakery sold 24 more cheese pies than beef pies. This is our golden ticket to figuring out the actual number of each type of pie sold. Remember, cheese pies represent 2/3 of the total, and beef pies represent 2/15 of the total. The difference between these two fractions corresponds to the 24-pie difference we're told about in the problem. To find this fractional difference, we subtract the fraction of beef pies from the fraction of cheese pies. So, the equation is (2/3) - (2/15).

Just like before, we need a common denominator to subtract these fractions. We already know that the least common denominator for 3 and 15 is 15. So, we convert 2/3 to 10/15. Now our equation is (10/15) - (2/15). Subtracting the fractions, we get (10 - 2)/15 = 8/15. This means that the difference of 24 pies represents 8/15 of the total number of pies sold. This fractional representation is crucial because it creates a direct link between a fraction of the total and a specific number of pies, allowing us to calculate the total number of pies. The relationship between the fractional difference and the actual number difference is the key to unlocking the solution.

Calculating the Total Number of Pies

Here's where the magic happens! We know that 8/15 of the total number of pies is equal to 24 pies. To find the total number of pies, we need to reverse this fraction. Think of it like this: if 8 slices out of 15 represent 24 pies, how many pies do all 15 slices represent? To find the total, we can set up a simple equation. Let's use 'x' to represent the total number of pies. So, our equation becomes (8/15) * x = 24.

To solve for x, we need to isolate x. We can do this by multiplying both sides of the equation by the reciprocal of 8/15, which is 15/8. So, the equation becomes x = 24 * (15/8). Now, we can simplify. 24 divided by 8 is 3. So, our equation simplifies to x = 3 * 15. Multiplying 3 by 15, we get x = 45. Therefore, the total number of pies sold at Leann's Bakery was 45. This calculation is a pivotal point in the problem-solving process, revealing the overall scale of the pie sale and enabling us to determine the number of each pie type sold.

Determining the Number of Each Pie Type

Now that we know the total number of pies sold is 45, we can figure out how many of each type of pie were sold. This involves going back to our original proportions: 2/3 of the pies were cheese, 1/5 were chicken, and 2/15 were beef. To find the number of cheese pies, we multiply the total number of pies (45) by the fraction representing cheese pies (2/3). So, the calculation is 45 * (2/3). 45 divided by 3 is 15, so we have 15 * 2, which equals 30. Therefore, Leann's Bakery sold 30 cheese pies. Next, let's calculate the number of chicken pies. We multiply the total number of pies (45) by the fraction representing chicken pies (1/5). So, the calculation is 45 * (1/5). 45 divided by 5 is 9. Therefore, they sold 9 chicken pies.

Finally, we need to figure out the number of beef pies. We multiply the total number of pies (45) by the fraction representing beef pies (2/15). So, the calculation is 45 * (2/15). 45 divided by 15 is 3, so we have 3 * 2, which equals 6. Therefore, Leann's Bakery sold 6 beef pies. To double-check our work, we can add the number of each type of pie: 30 cheese pies + 9 chicken pies + 6 beef pies = 45 pies, which matches our total. This breakdown of pie types is crucial for the final calculation, as it provides the quantities needed to determine the total revenue from the pie sale.

Calculating the Total Money Collected

We've reached the grand finale! Now that we know the number of each type of pie sold, we can calculate the total money collected. Remember, each pie was sold for $5.00. To find the total revenue, we multiply the total number of pies sold (45) by the price per pie ($5.00). So, the calculation is 45 * $5.00. Multiplying 45 by 5, we get 225. Therefore, Leann's Bakery collected a total of $225 from the pie sale. This final calculation brings our mathematical journey to a successful conclusion, providing the answer to the original question and highlighting the practical application of fraction arithmetic in a real-world scenario.

So, there you have it! Leann's Bakery's pie sale was not only a delicious success but also a fun math problem. We've successfully navigated the fractions, proportions, and calculations to determine that they collected a total of $225. Who knew pie could be so mathematically engaging, guys? Until next time, keep those calculations coming, and maybe treat yourself to a slice of pie – you've earned it!