Question

problem 6a
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.

complete the table showing three ways the truck can be packed with tables and chairs.
(table with columns: number of tables, t; number of chairs, c. rows: t=1 (c empty), c=60 (t empty), t=20 (c empty))

Explanation:

Step1: Find c when t=1

The total weight equation is \(50t + 10c = 1000\). Substitute \(t = 1\):
\(50(1)+10c = 1000\)
\(50 + 10c = 1000\)
\(10c = 950\)
\(c = 95\)

Step2: Find t when c=60

Substitute \(c = 60\) into \(50t + 10c = 1000\):
\(50t + 10(60)=1000\)
\(50t + 600 = 1000\)
\(50t = 400\)
\(t = 8\)

Step3: Find c when t=20

Substitute \(t = 20\) into \(50t + 10c = 1000\):
\(50(20)+10c = 1000\)
\(1000 + 10c = 1000\)
\(10c = 0\)
\(c = 0\)

Answer:

Number of Tables, \( t \)	Number of Chairs, \( c \)
8	60
20	0