Question

problem 5
on the math test, jamal got 6 fewer correct answers than tina. tina got 27 questions right.
how many answers did jamal get right on the math test? which of the equations below represents this situation?
a. j - 6 = 27
b. 27 - 6 = j
c. j + 6 = 27
d. 6 + 27 = j

Explanation:

Step1: Analyze the relationship

Jamal got 6 fewer correct answers than Tina. Tina got 27 right. Let \( j \) be Jamal's correct answers. So Jamal's score plus 6 equals Tina's score, which gives \( j + 6 = 27 \), or rearranged, \( j=27 - 6 \), or \( 27-j = 6 \), or \( j=27 - 6 \) can also be written as \( j+6 = 27 \) (by adding 6 to both sides of \( j=27 - 6 \)). Let's check each option:
- Option A: \( j - 6 = 27 \) means Jamal has 6 more than Tina, which is wrong.
- Option B: \( 27 - 6 = j \) is correct as Jamal has 6 less than 27. But also, \( j+6 = 27 \) (Option C) is equivalent (adding 6 to both sides of \( j=27 - 6 \)). Wait, let's re - express. If Jamal has \( j \) correct, and he has 6 fewer than Tina (27), then \( j=27 - 6 \), which can be rewritten as \( j + 6=27 \) (by adding 6 to both sides). Let's check the options again:
- Option A: \( j-6 = 27 \) → Jamal's score minus 6 is Tina's, which is wrong.
- Option B: \( 27 - 6=j \) → This is correct as Jamal has 6 less than 27. But also, \( j + 6=27 \) (Option C) is the same equation rearranged. Wait, maybe I made a mistake. Let's think again. The problem says "Jamal got 6 fewer correct answers than Tina. Tina got 27 questions right." So Jamal's correct answers \( j=27 - 6 \), which is \( 27-6 = j \) (Option B) or \( j + 6=27 \) (Option C). Wait, maybe the question is about which equation represents the situation. Let's check the equations:
- For Option C: \( j+6 = 27 \) → If we solve for \( j \), we get \( j=27 - 6 \), which is Jamal's score (since he has 6 less than 27).
- Option B: \( 27 - 6=j \) is also correct. But maybe the intended answer is Option C or B? Wait, let's check the equations again. Let's take Option C: \( j + 6=27 \). If we subtract 6 from both sides, we get \( j=27 - 6 \), which is Jamal's score. Option B: \( 27-6 = j \) is directly stating Jamal's score is 27 minus 6. Both B and C are correct in terms of the relationship, but maybe the question is looking for the equation that represents "Jamal's score plus 6 equals Tina's score". So \( j+6 = 27 \) (Option C) is the equation that shows that when we add the 6 fewer answers Jamal had to his score, we get Tina's score. Option B is \( 27 - 6=j \), which is also correct. Wait, maybe there is a mis - analysis. Let's check the options again:
- Option A: \( j - 6=27 \): Jamal's score minus 6 is Tina's, which is wrong.
- Option B: \( 27 - 6=j \): Tina's score minus 6 is Jamal's, correct.
- Option C: \( j + 6=27 \): Jamal's score plus 6 is Tina's, correct.
- Option D: \( 6 + 27=j \): 6 plus Tina's score is Jamal's, which is wrong (Jamal has less than Tina).
But maybe the question is designed to have \( j+6 = 27 \) as the correct equation because it shows the relationship of Jamal's score plus the 6 he was short of Tina's score equals Tina's score. So the correct equation is \( j + 6=27 \) (Option C) or \( 27-6 = j \) (Option B). But let's re - read the question: "Which of the equations below represents this situation?". Let's model the situation: Let \( j \) be Jamal's correct answers. Tina's correct answers = Jamal's correct answers+6. Tina's correct answers are 27. So \( 27=j + 6 \), which is \( j + 6=27 \) (Option C).

Step2: Evaluate each option

- Option A: \( j-6 = 27 \) implies \( j=33 \), which would mean Jamal got more than Tina, wrong.
- Option B: \( 27 - 6=j \) gives \( j = 21 \), which is correct numerically, but the equation structure: it's Tina's score minus 6 equals Jamal's.
- Option C: \( j + 6=27 \) can be solved to \( j=21 \), and it represents that Jamal's score plus 6 (the number he was short) equals Tina's score, which is the correct relationship.
- Option D: \( 6 + 27=j \) gives \( j = 33 \), which is wrong as Jamal has fewer than Tina.

Answer:

C. \( j + 6=27 \)