Five tables and eight chairs cost $115, while three tables and five chairs cost $70. Determine the cost of each table and each chair.
Let's call the cost of one table "t" and the cost of one chair "c".
From the first sentence, we can set up the equation:
5t + 8c = 115
From the second sentence, we can set up another equation:
3t + 5c = 70
Now we have two equations with two variables, which we can solve using elimination or substitution. Let's use substitution:
Solve the second equation for one variable:
3t + 5c = 70
3t = 70 - 5c
t = (70 - 5c)/3
Now substitute this expression for t into the first equation:
5t + 8c = 115
5((70 - 5c)/3) + 8c = 115
Multiply both sides by 3 to get rid of the fraction:
5(70 - 5c) + 24c = 345
Expand:
350 - 25c + 24c = 345
Simplify:
-c = -5
c = 5
Now we can plug in c = 5 to find t:
3t + 5c = 70
3t + 5(5) = 70
3t + 25 = 70
3t = 45
t = 15
So each table costs $15 and each chair costs $5.