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)
Let's assume the cost of each table is x and the cost of each chair is y.
According to the given information, the discount store is selling 5 small tables with 8 chairs for $115.
So, the cost of 5 tables and 8 chairs is 115 dollars.
5x + 8y = 115 --------(Equation 1)
Again, it is also given that three tables with 5 chairs cost $70.
So, the cost of 3 tables and 5 chairs is 70 dollars.
3x + 5y = 70 -----------(Equation 2)
Now, we need to solve these two simultaneous equations to find the values of x and y.
We can solve this system of equations using the method of substitution or elimination.
Let's use the method of substitution:
From Equation 1, we get:
5x + 8y = 115
=> 8y = 115 - 5x
=> y = (115 - 5x)/8
Now, substitute this value of y in Equation 2:
3x + 5((115 - 5x)/8) = 70
Multiply both sides of the equation by 8 to eliminate the fraction:
24x + 5(115 - 5x) = 560
24x + 575 - 25x = 560
-x = 560 - 575
-x = -15
=> x = 15
Substituting this value of x in Equation 2:
3(15) + 5y = 70
45 + 5y = 70
5y = 70 - 45
5y = 25
=> y = 5
So, the cost of each table (x) is $15 and the cost of each chair (y) is $5.