Final answer:
The vendor sold 80 hot dogs and 160 sodas at the basketball game. A system of equations based on the given totals and the relationship between the number of hot dogs and sodas was used to determine this.
Step-by-step explanation:
Let's assume the number of hot dogs sold is x. According to the problem, the number of sodas sold is two times the number of hot dogs, so the sodas would be 2x. Together, the total number of sodas and hot dogs sold was 240. So, the equation to solve would be x + 2x = 240.
Combining like terms, we have 3x representing the total number of products sold. To find the value of x, we divide both sides of the equation by 3: 3x/3 = 240/3, simplifying to x = 80. Therefore, 80 hot dogs were sold.
To find the number of sodas sold, we multiply the number of hot dogs by 2: 2 * 80 == 160. So, 160 sodas were sold.
Summing up, the vendor sold 80 hot dogs and 160 sodas.