Let's solve this problem step-by-step using algebra:
Let's represent the number of hot dogs sold as 'h', and the number of sodas sold as 's'.
Given information:
The number of sodas sold was two times the number of hot dogs sold:
s = 2h
The total number of items sold (sodas + hot dogs) is not specified, so let's represent it as 'total'.
Since we know that the total number of items sold is the sum of sodas and hot dogs, we can write an equation for it:
total = s + h
Now, we can substitute the value of 's' from the first equation into the second equation:
total = (2h) + h
Simplifying the equation:
total = 3h
Now, we have an equation relating the total number of items sold to the number of hot dogs sold.
To find the values of 's' and 'h', we need more information. If we knew the specific value of 'total', we could use the equation 'total = 3h' to find the number of hot dogs (h), and then use 's = 2h' to find the number of sodas (s).
For example, if the total number of items sold ('total') is 60, we can find the values of 's' and 'h':
total = 3h
60 = 3h
Now, solve for 'h':
h = 60 / 3
h = 20
Now, use the value of 'h' to find 's':
s = 2h
s = 2 * 20
s = 40
So, if the total number of items sold is 60, the vendor sold 40 sodas and 20 hot dogs. However, without knowing the specific value of 'total', we cannot determine the exact number of sodas and hot dogs sold.