Let \( x \) be the number of chicken wings. According to the problem, the number of mini hotdogs is \( x + 10 \).
Since each mini hotdog has 70 calories and each chicken wing has 60 calories, we can express the total calorie count as follows:
\[ 70(x + 10) + 60x = 1220 \]
Expanding this equation, we have:
\[ 70x + 700 + 60x = 1220 \]
Combining like terms:
\[ 130x + 700 = 1220 \]
Next, we subtract 700 from both sides:
\[ 130x = 520 \]
Now, we divide both sides by 130 to solve for \( x \):
\[ x = \frac{520}{130} = 4 \]
So, \( x \), the number of chicken wings, is 4. Next, we find the number of mini hotdogs:
\[ x + 10 = 4 + 10 = 14 \]
Thus, the number of mini hotdogs is 14.
To summarize:
- Number of mini hotdogs: \( 14 \)
- Number of chicken wings: \( 4 \)
Finally, we can verify the total calories:
\[ 70 \times 14 + 60 \times 4 = 980 + 240 = 1220 \]
The calculations are consistent. Therefore, the solution is: \[ \text{Number of mini hotdogs: } \boxed{14} \] \[ \text{Number of chicken wings: } \boxed{4} \]