Question

for every 8 guests at a dinner party, there is 1 table. which statement about the number of guests and tables must be true? there will be 7 times as many guests as tables. there will be 8 times as many guests as tables. there will be 7 more guests than tables. there will be 8 more guests than tables.

Explanation:

Step1: Analyze the relationship

Given that for every 8 guests, there is 1 table. Let the number of tables be \( t \), then the number of guests \( g = 8t \). So the number of guests is 8 times the number of tables.

Step2: Evaluate each option

• Option 1: "There will be 7 times as many guests as tables." Incorrect, since \( g = 8t \), it's 8 times, not 7.
• Option 2: "There will be 8 times as many guests as tables." Correct, as \( g = 8t \).
• Option 3: "There will be 7 more guests than tables." Let \( t = 1 \), guests \( = 8 \), \( 8 - 1 = 7 \), but if \( t = 2 \), guests \( = 16 \), \( 16 - 2 = 14

eq 7 \), so this is not always true.

• Option 4: "There will be 8 more guests than tables." For \( t = 1 \), \( 8 - 1 = 7

eq 8 \), so incorrect.

Answer:

The correct option is: There will be 8 times as many guests as tables.