At a hockey game, a vender sold a combined total of 246 sodas and hot dogs. The number of hot dogs sold was 46 less than the number of sodas 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.
According to the information given, we have two equations:
1) x + y = 246
2) y = x - 46
Substitute equation 2 into equation 1:
x + (x - 46) = 246
2x - 46 = 246
2x = 292
x = 146
Now, plug in the value of x back into equation 2 to find y:
y = 146 - 46
y = 100
Therefore, the number of sodas sold was 146 and the number of hot dogs sold was 100.