# 3.1. Condition:

Vanya bought balloons, red ones were 7 times more than blue ones. While Vanya was walking home, some of the balloons burst, and among the burst balloons, there were 3 times fewer red ones than blue ones. What is the smallest number of balloons Vanya could have bought?
# Answer: 24

## Solution.

Notice that at least one red balloon has burst, which means at least three blue balloons have burst. Therefore, there are at least three blue balloons, which means there are at least $7 \cdot 3=21$ red balloons, so the total number of balloons must be at least 24. For example, Vanya could have been carrying 21 red balloons and 3 blue ones, and 1 red balloon and all 3 blue balloons could have burst.

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