Final answer:
To find the number of round and rectangular tables needed, we can set up a system of equations using the given information. By solving the system of equations, we find that you should rent 1 round table and 4 rectangular tables for your dinner party.
Step-by-step explanation:
To find the number of round and rectangular tables needed, we need to determine how many people can be seated at each type of table. With each round table seating 8 people and each rectangular table seating 12, we can write two equations to represent the number of people seated:
Let r be the number of round tables and let s be the number of rectangular tables. The total number of people seated is given as 56.
Equation 1: 8r + 12s = 56
We also know that the total number of tables rented is 5, so the sum of the round tables and rectangular tables should be equal to 5:
Equation 2: r + s = 5
To solve this system of equations, we can use the substitution method or the elimination method.
Start by solving Equation 2 for r:
r = 5 - s
Substitute this expression for r into Equation 1:
8(5 - s) + 12s = 56
Distribute:
40 - 8s + 12s = 56
Combine like terms:
4s = 16
Divide both sides by 4:
s = 4
Now substitute this value of s back into Equation 2 to find r:
r + 4 = 5
Subtract 4 from both sides:
r = 1
Therefore, you should rent 1 round table and 4 rectangular tables for your formal birthday dinner party.