Final answer:
The smaller ball of string is the better buy because its price per unit diameter is lower.
Step-by-step explanation:
The ball of string with the larger diameter is the better buy.
Let's assume the diameter of the smaller ball is x. According to the question, the diameter of the larger ball is 1.5 times the diameter of the smaller ball, so its diameter is 1.5x.
The price of the smaller ball of string is $1.49. If we compare the prices per unit diameter, the price of the smaller ball per unit diameter is 1.49/x dollars. The price of the larger ball of string is $4.99, and its price per unit diameter is 4.99/(1.5x) dollars. Since 1.49/x is less than 4.99/(1.5x), the smaller ball of string is the better buy.