## 29. Pretzels and Pretzelkins

- Here's another problem,—began the Gryphon. One day, the Mock Turtle went to the store to buy pretzels for the next tea party.
- How much are your pretzels?—he asked the store owner.
- The price depends on the size: I can offer you small pretzelkins and large pretzels. One pretzel costs as much as three pretzelkins.
- How much do seven pretzels and four pretzelkins cost?—asked the Mock Turtle.
- Twelve cents more than four pretzels and seven pretzelkins,—came the mysterious answer.

![](https://cdn.mathpix.com/cropped/2024_05_21_5afa4e43618f5800e92dg-048.jpg?height=677&width=782&top_left_y=267&top_left_x=657)

How much does one pretzel cost?
29. Pretzels and pretzelkins. Since each pretzel costs as much as one pretzelkin, 7 pretzels cost as much as 21 pretzelkins, and 7 pretzels and 4 pretzelkins cost as much as 25 pretzelkins. On the other hand, 4 pretzels and 7 pretzelkins cost as much as 19 pretzelkins (since 4 pretzels cost as much as 12 pretzelkins). Thus, the difference in cost between 25 and 19 pretzelkins is 12 cents. Therefore, 6 pretzelkins (25-19=6) cost 12 cents, 1 pretzelkin costs 2 cents, and 1 pretzel costs 6 cents.

Verification. 4 pretzels and 7 pretzelkins cost $24+14=38$ cents, and 7 pretzels and 4 pretzelkins cost $42+8=50$ cents, which is indeed 12 cents more than in the first case.