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Feature
Solving a Linear System
A discount store is selling 5 small tables with 8 chairs for $115. Three tables with 5 chairs cost $70.
Question 1
Which system of linear equations could be used to find the cost of each table (x) and the cost of each chair (y)?
Responses
A 3x + 8y = $70; 8x + 3y = $1153x + 8y = $70; 8x + 3y = $115
B 5x + 8y = $115; 3x + 5y = $705x + 8y = $115; 3x + 5y = $70
C 5x + 8y = $115; 2x − 5y = $705x + 8y = $115; 2x − 5y = $70
D 8x + 5y = $115; 5x + 3y = $708x + 5y = $115; 5x + 3y = $70
Question 2
Determine the cost of each table (x) and the cost of each chair (y).
To determine the cost of each table (x) and the cost of each chair (y), we need to solve the system of linear equations.
The correct system of linear equations is option B:
5x + 8y = $115
3x + 5y = $70
Solving this system of equations will give us the values of x and y.
To solve this system, we can use any method such as substitution or elimination. I will use the elimination method here.
Multiplying the first equation by 3 and the second equation by 5, we can eliminate the x term:
15x + 24y = $345
15x + 25y = $350
Subtracting the first equation from the second equation:
15x + 25y - (15x + 24y) = $350 - $345
y = $5
Substituting the value of y back into the first equation:
5x + 8($5) = $115
5x + $40 = $115
5x = $115 - $40
5x = $75
x = $15
Therefore, the cost of each table (x) is $15 and the cost of each chair (y) is $5.