# Problem 1. (4 points)

In the run-up to the New Year, a fair is being held at the school where students exchange festive toys. As a result, the following exchange norms have been established:

1 Christmas tree ornament can be exchanged for 2 crackers, 5 sparklers can be exchanged for 2 garlands, and 4 Christmas tree ornaments can be exchanged for 1 garland.

a) How many crackers can be obtained for 10 sparklers? (1 point)

b) Which is more valuable: 5 Christmas tree ornaments and 1 cracker or 2 sparklers? (3 points)

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# Solution:

a) 10 sparklers $=4$ garlands = 16 ornaments = $\mathbf{32}$ crackers. (1 point)

b) Convert everything to crackers. In the first case, we have $\mathbf{11}$ crackers. In the second case, 2 sparklers $=4 / 5$ garlands $=16 / 5$ ornaments $=32 / 5$ crackers $=\mathbf{6.4}$ crackers. Answer: 5 ornaments and 1 cracker are more expensive than 2 sparklers. (1 point for converting each set to a single unit + 1 point for the correct answer)