A discount store is selling 5 small tables with 8 chairs for $115. Three tables with 5 chairs cost $70
Determine the cost of each table (x) and the cost of each chair (y)
A: x = $15; y = $5
B: x = $10; y = $5
C: x = $5; y = $10
D: x = $12; y = $3
Let's determine the cost of each table (x) and the cost of each chair (y) using a system of equations.
Let x be the cost of each table and y be the cost of each chair.
From the first piece of information, we know that 5x + 8y = 115.
From the second piece of information, we know that 3x + 5y = 70.
To solve this system of equations, we can use the substitution method.
First, let's solve the second equation for x:
3x + 5y = 70
3x = 70 - 5y
x = (70 - 5y)/3
Now substitute this value for x in the first equation:
5((70 - 5y)/3) + 8y = 115
(350 - 25y)/3 + 8y = 115
Multiply through by 3 to eliminate the denominator:
350 - 25y + 24y = 345
Combine like terms:
-25y + 24y = 345 - 350
-y = -5
y = 5
Now substitute this value for y in the second equation to solve for x:
3x + 5(5) = 70
3x + 25 = 70
3x = 70 - 25
3x = 45
x = 45/3
x = 15
Therefore, the correct answer is choice A: x = $15; y = $5.