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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
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).
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)
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.
The correct student is Student 1.
To find an equivalent expression using the distributive property, we need to multiply the term outside the parentheses with each term inside the parentheses.
Student 1 correctly distributed the -3 to both terms inside the parentheses:
8 - 3(2+4k) = 8 - 6 - 12k
However, both Student 2 and Student 3 made mistakes.
In Student 2's work, they distributed the -3 to only the first term inside the parentheses and forgot to distribute it to the second term:
8 - 3(2+4k) = 8 - 6 - 3(4k) = 8 - 6 - 12k
In Student 3's work, they made two mistakes. First, they distributed the -3 to only the first term inside the parentheses and forgot to distribute it to the second term:
8 - 3(2+4k) = 8 - 6 - 3(4k) = 8 - 6 - 12k
Second, they made an error in simplifying the expression. Instead of correctly combining like terms, they mistakenly wrote -10k as the final expression.
Therefore, Student 1 is the only student with the correct work.