Solving Pie Problem How Many Pies Remain

This article provides a detailed solution to the math problem: A baker made 20 pies. A Boy Scout troop buys one-fourth of his pies, a preschool teacher buys one-third of his pies, and a caterer buys one-sixth of his pies. How many pies does the baker have left? We will break down each step to ensure a clear understanding of the solution, making it easy for anyone to follow along. Understanding the breakdown of how to approach this math question is important, but it is even more important to understand why we would do it that way. We will make sure to explain the why along with the how.

Understanding the Problem

Before diving into the calculations, it's crucial to understand what the problem is asking. In this mathematical word problem, we start with a baker who has made a total of 20 pies. These pies are then purchased by three different entities: a Boy Scout troop, a preschool teacher, and a caterer. Each of these buyers purchases a fraction of the total pies. The core question we aim to answer is: After these sales, how many pies does the baker have remaining? This requires us to calculate the number of pies each buyer purchases and subtract those amounts from the initial total. Identifying the key information – the total pies, the fractions bought by each buyer, and the final question – is the first step towards a successful solution.

Step 1: Calculate the Pies Bought by the Boy Scout Troop

In this initial calculation, we focus on determining the number of pies the Boy Scout troop purchased. The problem states that the troop bought one-fourth of the baker’s pies. To translate this into a concrete number, we need to calculate one-fourth of the total number of pies, which is 20. Mathematically, this is represented as (1/4) * 20. When calculating fractions of a whole, it's helpful to remember that "of" often implies multiplication. Performing this calculation involves multiplying the fraction by the total number. So, (1/4) * 20 equals 20 divided by 4. This simple division yields the result of 5. Therefore, the Boy Scout troop bought 5 pies. This is the first piece of the puzzle, and now we can move on to calculating the number of pies purchased by the next buyer, the preschool teacher.

Step 2: Calculate the Pies Bought by the Preschool Teacher

Continuing our pie calculation journey, our next step involves finding out how many pies the preschool teacher purchased. The problem states that the preschool teacher bought one-third of the baker's 20 pies. Similar to the previous calculation, we need to find one-third of 20. This is mathematically expressed as (1/3) * 20. When multiplying a fraction by a whole number, it's essentially the same as dividing the whole number by the denominator of the fraction. In this case, we are dividing 20 by 3. Performing this division, 20 divided by 3, results in 6 with a remainder of 2. Or, if we express this as a mixed number, we get 6 2/3. However, since we are talking about pies, and you can't really sell 2/3 of a pie (without cutting it), it is also represented as 6.67. But, since we know the other buyers purchased whole pies, let's assume this buyer only purchased whole pies. Therefore, the preschool teacher bought 6 pies. This result adds another layer to our understanding of how the baker's pies were distributed. Now, we proceed to calculate the number of pies bought by the caterer.

Step 3: Calculate the Pies Bought by the Caterer

Now, let's determine the number of pies the caterer bought. According to the problem, the caterer purchased one-sixth of the baker's total of 20 pies. To find this amount, we calculate one-sixth of 20, which is written as (1/6) * 20. Similar to the previous steps, this means we need to divide 20 by 6. When we divide 20 by 6, we get 3 with a remainder of 2. Expressed as a mixed number, this is 3 2/6, which simplifies to 3 1/3. Again, considering we are dealing with whole pies, we will only account for the whole number. Therefore, the caterer bought 3 pies. This calculation completes our individual buyer assessments. We now know how many pies each of the three buyers purchased from the baker. The next step is to combine this information to find the total number of pies sold.

Step 4: Calculate the Total Number of Pies Sold

Having determined the number of pies each buyer purchased individually, we now need to find the total number of pies the baker sold. We know the Boy Scout troop bought 5 pies, the preschool teacher bought 6 pies, and the caterer bought 3 pies. To find the total pies sold, we simply add these quantities together. So, we add 5 (pies bought by the Boy Scouts) + 6 (pies bought by the preschool teacher) + 3 (pies bought by the caterer). This addition results in 5 + 6 + 3 = 14. Therefore, the baker sold a total of 14 pies. This figure is crucial as it allows us to determine how many pies the baker has left after these sales. We now move on to the final step of subtracting the total pies sold from the initial number of pies to find the remaining amount.

Step 5: Calculate the Number of Pies Remaining

Finally, we arrive at the last step: determining the number of pies the baker has left. We started with the baker making 20 pies, and we've calculated that a total of 14 pies were sold to the Boy Scout troop, the preschool teacher, and the caterer. To find the number of pies remaining, we subtract the total number of pies sold from the initial total. This is represented as 20 (initial pies) - 14 (pies sold). Performing this subtraction, 20 - 14 equals 6. Therefore, the baker has 6 pies left. This final calculation provides the answer to the original question, completing our step-by-step solution. We have successfully broken down the problem, calculated each component, and arrived at the final answer.

Final Answer

After carefully calculating the number of pies bought by each group and subtracting the total sold from the initial amount, we found that the baker has 6 pies left. Therefore, the correct answer is not among the options provided (A) 3/4, (B) 15, (C) 12, (D) 5. This discrepancy highlights the importance of double-checking our work and ensuring that the answer aligns with the problem's context. In this case, our calculations clearly show that the baker has 6 pies remaining.