Final answer:
To find the number of female guests at the party, we can set up and solve two equations using the given information.
Step-by-step explanation:
To solve this problem, we can let the number of male guests be represented by the variable 'm' and the number of female guests be represented by the variable 'f'.
According to the information given, we have the equation: f = 4m - 11.
We also know that there are a total of 14 guests, so we have the equation: m + f = 14.
By substituting the value of f from the first equation into the second equation, we can solve for the number of male guests and then find the number of female guests.
Let's do the calculations:
m + (4m - 11) = 14
5m - 11 = 14
5m = 25
m = 5
Now, substituting this value back into the first equation, we can find the number of female guests:
f = 4(5) - 11
f = 20 - 11
f = 9
Therefore, there are 9 female guests at the party.