At a football game, a vender sold a combined total of 128 sodas and hot dogs. The number of sodas sold was 34 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.
Let's represent the number of sodas sold as "x" and the number of hot dogs sold as "y".
From the given information, we can create a system of equations:
1) x + y = 128 (since the total number of sodas and hot dogs sold is 128)
2) x = y + 34 (since the number of sodas sold is 34 more than the number of hot dogs sold)
Substitute the value of x from equation 2 into equation 1:
y + 34 + y = 128
2y + 34 = 128
2y = 94
y = 47
Now, substitute the value of y back into equation 2 to find x:
x = 47 + 34
x = 81
Therefore, the number of sodas sold was 81 and the number of hot dogs sold was 47.