Solving a Mathematical Puzzle: How Many Pies Did Mrs. Jenny Make?

Mrs. Jenny's pie-making adventure presents a fascinating mathematical puzzle. She crafts both chicken and potato pies, with a specific ratio of one type to the other. Let's break down the puzzle to understand how many pies she made and how many she had left after selling a certain portion of them.

The Puzzle Details

Mrs. Jenny makes a total of 3/8 of her pies as chicken pies, and the remaining 5/8 are potato pies. After selling half of the chicken pies and three-quarters of the potato pies, she ends up with 22 pies left over. The challenge is to figure out how many pies she made initially.

Step-by-Step Solution

To solve this, we start by letting x represent the total number of pies Mrs. Jenny made. We can then calculate the number of each type of pie:

Number of chicken pies: 3/8x Number of potato pies: 5/8x

Next, we calculate how many of each type of pie she sold:

Chicken pies sold: Potato pies sold:

Let's break down the calculations:

Calculating the Chicken Pies Sold

Mrs. Jenny sold half of the chicken pies:

1/2 × 3/8x 3/16x

This means that the remaining chicken pies are:

3/8x - 3/16x 6/16x - 3/16x 3/16x

Calculating the Potato Pies Sold

Mrs. Jenny sold three-quarters of the potato pies:

3/4 × 5/8x 15/32x

This means that the remaining potato pies are:

5/8x - 15/32x 20/32x - 15/32x 5/32x

Total Pies Sold

The total number of pies sold is the sum of the chicken and potato pies sold:

3/16x 15/32x 6/32x 15/32x 21/32x

Calculating the Number of Pies Left

The number of pies left is the total number of pies minus the total number of pies sold:

x - 21/32x 32/32x - 21/32x 11/32x

Solving for x

We know that Mrs. Jenny had 22 pies left:

11/32x 22

Multiplying both sides by 32/11 to solve for x gives:

x 22 × 32/11 2 × 32 64

Therefore, the total number of pies Mrs. Jenny made is 64.

Mathematical Insight

This puzzle showcases the application of fractions and algebra to solve real-world problems. It's a great exercise to practice understanding and manipulating fractions, and to apply algebraic techniques to find an unknown value.

Conclusion

Using logical reasoning and mathematical calculations, we have determined that Mrs. Jenny made a total of 64 potato and chicken pies. This solution exemplifies the power of mathematical problem-solving in various contexts.