Question

You invited 56 people to your formal birthday dinner party. You can afford to rent 5 tables, round or rectangular (each costing the same amount ). Each round table can seat 8 people and each rectangular table can seat 12. How many round and rectangular tables should you rent?

Answer 1

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.