Aunt Lola's Cakes: How Many Strawberry?

Alright, guys, let's dive into a sweet mathematical problem! Aunt Lola, bless her heart, has been baking up a storm. We know she's made a bunch of cakes, and they're divided into three delicious flavors: pineapple, strawberry, and coconut. The challenge is to figure out exactly how many strawberry cakes she baked. Sounds easy? Well, there's a bit of fraction fun involved!

Cracking the Cake Code: Fractions and Proportions

First things first, let's break down what we know. Aunt Lola's cake distribution looks like this:

• Pineapple cakes make up 3/7 of the total.
• Strawberry cakes account for 2/5 of the total.
• The remaining cakes are coconut flavored.

And here's the kicker: there are 252 more pineapple cakes than coconut cakes. This is our golden ticket to solving the puzzle! To solve this type of problem effectively, you need to understand the relationship between fractions, proportions, and the whole. In this case, the 'whole' represents the total number of cakes Aunt Lola baked. Each fraction (3/7, 2/5) represents a portion of this whole. The key to unlocking the solution lies in finding a common denominator to easily compare these fractions and determine the fraction representing the coconut cakes. Once we know all the fractional parts, we can use the information about the difference between pineapple and coconut cakes to find the actual number of strawberry cakes. So, grab your thinking caps, and let's get started on this delicious math adventure!

Finding the Missing Piece: Coconut Cake Fraction

Before we can compare pineapple and coconut cakes directly, we need to figure out what fraction of the total is represented by coconut cakes. Since the fractions of pineapple, strawberry, and coconut cakes must add up to 1 (representing the whole), we can calculate the coconut fraction. This involves a bit of fraction arithmetic, but don't worry, we'll take it step by step.

To find the coconut fraction, we'll subtract the fractions of pineapple and strawberry cakes from 1:

1 - (3/7) - (2/5)

To do this subtraction, we need to find a common denominator for 7 and 5, which is 35. So we convert the fractions:

(3/7) = (15/35)

(2/5) = (14/35)

Now we can rewrite the equation as:

1 - (15/35) - (14/35)

To subtract from 1, we express 1 as a fraction with the same denominator:

(35/35) - (15/35) - (14/35) = (35 - 15 - 14) / 35 = (6/35)

So, coconut cakes make up 6/35 of the total. Now we're one step closer to uncovering the mystery of Aunt Lola's strawberry cakes!

Pineapple vs. Coconut: The 252 Difference

Now we know that pineapple cakes represent 3/7 (or 15/35) of the total, and coconut cakes represent 6/35. The problem tells us that there are 252 more pineapple cakes than coconut cakes. This difference is crucial! It allows us to connect the fractional difference to a concrete number, which will help us find the value of one 'fractional unit' and ultimately, the total number of cakes.

The difference in fractions between pineapple and coconut is:

(15/35) - (6/35) = (9/35)

This means that 9/35 of the total number of cakes corresponds to 252 cakes. In other words, 9 parts out of 35 represent 252 cakes. Now we can set up an equation to find out what one 'part' (1/35) represents:

(9/35) * Total = 252

To find the 'Total,' we can rearrange the equation:

Total = 252 / (9/35) = 252 * (35/9)

Let's simplify this calculation to find the total number of cakes Aunt Lola baked. This will be the key to unlocking the exact number of strawberry cakes!

Unveiling the Total: How Many Cakes in All?

Let's calculate the total number of cakes. We've established that:

Total = 252 * (35/9)

First, we can simplify by dividing 252 by 9:

252 / 9 = 28

Now we multiply 28 by 35:

28 * 35 = 980

So, the total number of cakes Aunt Lola baked is 980. Now that we know the total, we can finally calculate the number of strawberry cakes. Remember, strawberry cakes make up 2/5 of the total. So, the next step is to apply this fraction to the total number of cakes.

Knowing the total number of cakes is like having the whole pie – now we just need to figure out how big the strawberry slice is!

The Grand Finale: Calculating Strawberry Cakes

We know that strawberry cakes represent 2/5 of the total, and we've calculated that the total number of cakes is 980. To find the number of strawberry cakes, we simply multiply the fraction by the total:

Number of Strawberry Cakes = (2/5) * 980

First, we can divide 980 by 5:

980 / 5 = 196

Now, multiply 196 by 2:

196 * 2 = 392

Therefore, Aunt Lola baked 392 strawberry cakes! We've finally solved the mystery. What a delicious journey through fractions and proportions. I hope you've enjoyed untangling this sweet mathematical problem as much as I have! Remember, math can be fun, especially when it involves cakes!

Aunt Lola's Baking Secrets: A Recap

Let's recap how we cracked Aunt Lola's cake conundrum:

1. Identified the fractions: We knew pineapple (3/7), strawberry (2/5), and needed to find coconut.
2. Found the coconut fraction: We subtracted pineapple and strawberry fractions from 1 to get 6/35.
3. Compared pineapple and coconut: The difference (9/35) represented 252 cakes.
4. Calculated the total: We used the difference to find that Aunt Lola baked 980 cakes in total.
5. Solved for strawberry: We multiplied the total by the strawberry fraction (2/5) to find 392 strawberry cakes.

So, the final answer is: Aunt Lola baked 392 strawberry cakes. High five for solving the puzzle! Now, who's up for a slice?