Question

1. extension question a truck delivers tables and chairs for a fair. the truck can carry 1,000 pounds total.

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

a. complete the table showing three ways the truck can be packed with tables and chairs.

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

b. write an equation that represents the number of tables, t, and the number of chairs, c, that the truck can carry.

Explanation:

Part a: Completing the table

Step 1: For \( t = 1 \)

The total weight the truck can carry is 1000 pounds. Each table weighs 50 pounds and each chair weighs 10 pounds. Let the number of chairs be \( c \). The weight of tables is \( 50\times1 = 50 \) pounds. The weight of chairs is \( 10c \) pounds. So, \( 50 + 10c=1000 \). Subtract 50 from both sides: \( 10c = 1000 - 50 = 950 \). Then \( c=\frac{950}{10}=95 \).

Step 2: For \( c = 60 \)

The weight of chairs is \( 10\times60 = 600 \) pounds. Let the number of tables be \( t \). The weight of tables is \( 50t \) pounds. So, \( 50t+600 = 1000 \). Subtract 600 from both sides: \( 50t=1000 - 600 = 400 \). Then \( t=\frac{400}{50}=8 \).

Step 3: For \( t = 20 \)

The weight of tables is \( 50\times20 = 1000 \) pounds. Let the number of chairs be \( c \). The weight of chairs is \( 10c \) pounds. So, \( 1000+10c = 1000 \). Subtract 1000 from both sides: \( 10c=0 \), so \( c = 0 \).

The completed table (rows from top to bottom):

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

Part b: Writing the equation

Step 1: Define the weights

The weight of \( t \) tables is \( 50t \) pounds (since each table is 50 pounds) and the weight of \( c \) chairs is \( 10c \) pounds (since each chair is 10 pounds).

Step 2: Total weight equation

The sum of the weight of tables and chairs should equal the total weight the truck can carry (1000 pounds). So the equation is \( 50t + 10c=1000 \). We can also simplify it by dividing both sides by 10: \( 5t + c = 100 \), or \( c=100 - 5t \) or \( t = \frac{1000 - 10c}{50}=20-\frac{c}{5} \). But the standard form from the weight balance is \( 50t + 10c = 1000 \).

Answer:

Part a:

The completed table has values (from top row to bottom row for \( c \) or \( t \)): 95, 8, 0.

Part b:

The equation is \( \boldsymbol{50t + 10c = 1000} \) (or simplified forms like \( 5t + c = 100 \), \( c = 100 - 5t \), etc.)