A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 2 tables is $18. The total cost to rent 3 chairs and 8 tables is $55 . What is the cost to rent each chair and each table?
To find the cost of renting each chair and each table, we need to set up a system of equations based on the given information.
Let's assume the cost of renting one chair is "c" and the cost of renting one table is "t".
From the first piece of information, we know that 5 chairs and 2 tables cost $18. So we can write the equation:
5c + 2t = 18 (Equation 1)
From the second piece of information, we know that 3 chairs and 8 tables cost $55. So we can write the equation:
3c + 8t = 55 (Equation 2)
Now, we can solve this system of equations using any suitable method, such as substitution or elimination. Let's use the elimination method:
Multiply Equation 1 by 8 and Equation 2 by 2 to make the coefficients of "t" in both equations the same:
40c + 16t = 144 (Equation 3)
6c + 16t = 110 (Equation 4)
Now, subtract Equation 4 from Equation 3 to eliminate "t":
(40c + 16t) - (6c + 16t) = 144 - 110
34c = 34
c = 1
Substitute the value of c = 1 back into Equation 1 (or Equation 2) to find the value of t:
5(1) + 2t = 18
5 + 2t = 18
2t = 13
t = 6.5
Therefore, the cost to rent each chair is $1 and the cost to rent each table is $6.5.
5 c + 2 t = 18
multiplying by 4 ... 20 c + 8 t = 72
3 c + 8 t = 55
solve the system for c and t
... subtract equations to eliminate t
... solve for c
... substitute back to find t