Question

error analysis a sports team with 17 members is planning an end - of - season awards banquet. it costs $6 for each meal. to find the total cost of the meals, the team uses the expression 6(g + 17), where g is the number of guests attending the banquet. one team member incorrectly claims that the expression is equivalent to 6g+17. use the distributive property to write an expression equivalent to 6(g + 17). what was the likely error?
use the distributive property to write an equivalent expression.
6(g + 17)=6g + 102 (simplify your answer)
what was the likely error?
a. the team member multiplied the terms in the parentheses.
b. the team member did not distribute the 6 to each term in the parentheses.
c. the team member added the 6 to 17
d. the team member added the 6 to each term in the parentheses.

Explanation:

Step1: Recall Distributive Property

The Distributive Property states that \( a(b + c)=ab + ac \). For \( 6(g + 17) \), we should distribute 6 to both \( g \) and 17, getting \( 6\times g+6\times17 = 6g + 102 \).

Step2: Analyze the Error

The incorrect expression is \( 6g + 17 \). Comparing to the correct distributed form (\( 6g+102 \)), we see that the 6 was not distributed to the 17 (i.e., \( 6\times17 \) was not done, instead 17 was left as is). So the team member did not distribute the 6 to each term in the parentheses.

Answer:

B. The team member did not distribute the 6 to each term in the parentheses.