Question

problem 6c
a truck delivers tables and chairs for a fair. the truck can carry 1000 pounds total.

• tables weigh 50 pounds each.
• chairs weigh 10 pounds each.

draw a graph of the number of tables, t, and the number of chairs, c, that the truck can carry.
here is your equation: 50t + 10c = 1000
here is your table:

number of tables, t	number of chairs, c
8	60
20	0

Explanation:

Step1: Analyze the equation

The equation is \(50t + 10c=1000\). We can simplify it to \(5t + c = 100\) or \(c=- 5t + 100\). This is a linear equation in slope - intercept form \(y = mx + b\) (here \(c\) is like \(y\), \(t\) is like \(x\), slope \(m=-5\), \(y\) - intercept \(b = 100\)).

Step2: Plot the points from the table

• For \(t = 1\), \(c=95\). So the point is \((1,95)\).
• For \(t = 8\), \(c = 60\). So the point is \((8,60)\).
• For \(t=20\), \(c = 0\). So the point is \((20,0)\). Also, when \(t = 0\), from \(c=-5t + 100\), we get \(c = 100\), so the point \((0,100)\) is also on the line.

Step3: Draw the line

Plot the points \((0,100)\), \((1,95)\), \((8,60)\), \((20,0)\) on the coordinate plane (where the x - axis is the number of tables \(t\) and the y - axis is the number of chairs \(c\)) and draw a straight line passing through these points. The line should start from \((0,100)\) (when there are no tables, the truck can carry 100 chairs) and end at \((20,0)\) (when there are no chairs, the truck can carry 20 tables), with a slope of - 5 (for each additional table, the number of chairs decreases by 5).

Answer:

To draw the graph, plot the points \((0,100)\), \((1,95)\), \((8,60)\), \((20,0)\) on the given coordinate grid (x - axis: number of tables \(t\), y - axis: number of chairs \(c\)) and draw a straight line through them.