4A. In a basket, there are red, white, and yellow flowers. The number of yellow flowers is not less than the number of white flowers and is not greater than one third of the number of red flowers. The total number of white and yellow flowers is not less than 55. Find the smallest number of red flowers.
Solution. Let there be $a$-yellow, $b$-white, and $c$-red flowers in the basket. From the condition of the problem, it follows that $a \geq b$ (1), $a \leq \frac{1}{3} c$ (2), and $a+b \geq 55$ (3). From (1) and (3), we get $2 a \geq 55$, from which $a \geq 28$, since $a \in \mathbb{N}$. Then, from (2), we get $c \geq 3 a \geq 3 \cdot 28=84$. Therefore, the smallest number of red flowers is 84.