1 of 11 of 1 Items

Question

Question 1
Students were asked to use the distributive property to write an equivalent expression for the expression 8−3(2+4k).

Their work is shown below. Identify the student with the correct work. For the answers that are incorrect, explain where the students made mistakes.

Student 1

8−3(2+4k)

8−6+12k

2+12k



Student 2:

8−3(2+4k)

8−6−12k

2−12k



Student 3:

8−3(2+4k)

8−6−12k
2−12k
−10k

Answer 1

The correct student is Student 1.

Explanation:

To use the distributive property, you need to distribute the -3 to both terms inside the parentheses (2 and 4k).

Student 1 correctly distributed the -3 to both terms:

-3(2) = -6
-3(4k) = -12k

Then, they simplified the expression:

8 - 6 + 12k = 2 + 12k

This is the correct equivalent expression for 8 - 3(2 + 4k).

Answer 2

Math Time is a tutoring company for pre-algebra students. The profit this company makes in a year is given by the expression 0.5(200+32s), where s is the total number of students enrolled.



Part A: Use the distributive property to write an equivalent expression.

(2 points)

Part B: What is the company's yearly profit if its enrollment is 30 students?(2 points)

Answer 3

Part A: Use the distributive property to write an equivalent expression.

The expression given is 0.5(200+32s). To simplify this expression using the distributive property, we need to distribute the 0.5 to both terms inside the parentheses:

0.5 * 200 + 0.5 * 32s

Which simplifies to:

100 + 16s

Therefore, the equivalent expression using the distributive property is 100 + 16s.

Part B: What is the company's yearly profit if its enrollment is 30 students?

To find the company's yearly profit when the enrollment is 30 students, we can substitute s with 30 in the expression 100 + 16s:

Profit = 100 + 16(30)
Profit = 100 + 480
Profit = 580

Therefore, the company's yearly profit when the enrollment is 30 students is $580.