Question

solving a linear system
a discount store is selling 5 small tables with 8 chairs for $115.
three tables with 5 chairs cost $70.

cost of each table (x) and the cost of each chair (y)?
a ( 3x + 8y = 570, 8x + 3y = 115 )
b ( 5x + 8y = 115, 3x + 5y = 70 )
c ( 5x + 8y = 115, 2x - 5y = 70 )
d ( 8x + 5y = 115, 5x + 3y = 70 )

determine the cost of each table (x) and the cost of each chair (y).
a ( x = 115, y = 5 )
b ( x = 10, y = 15 )
c ( x = 15, y = 10 )

Explanation:

Step1: Match equations to scenario

Let $x$ = cost of 1 table, $y$ = cost of 1 chair.
5 tables + 8 chairs = $115: $5x + 8y = 115$
3 tables + 5 chairs = $70: $3x + 5y = 70$
This matches option B.

Step2: Solve the linear system

Multiply first equation by 3: $15x + 24y = 345$
Multiply second equation by 5: $15x + 25y = 350$
Subtract first new equation from second:
$$(15x + 25y) - (15x + 24y) = 350 - 345$$
$y = 5$

Step3: Substitute $y=5$ to find $x$

Substitute $y=5$ into $3x + 5y = 70$:
$3x + 5(5) = 70$
$3x + 25 = 70$
$3x = 45$
$x = 15$
This matches option A.

Answer:

1. B. $5x + 8y = \$115; 3x + 5y = \$70$
2. A. $x = \$15, y = \$5$