Question

problem 3
on the math test, evan got 12 fewer correct answers than noah. noah got 40 questions right.
how many answers did evan get right on the math test? which of the equations below represents this situation?
a. $12 + 40 = e$

b. $e - 12 = 40$

c. $40 - 12 = e$

d. $e + 12 = 40$

Explanation:

Step1: Analyze the relationship

Evan got 12 fewer correct answers than Noah. Noah got 40 right. So Evan's correct answers (e) plus 12 equals Noah's 40.

Step2: Match the equation

The equation that represents this is \( e + 12 = 40 \), which is option D. Also, we can check other options:
- Option A: \( 12 + 40 = e \) implies Evan got more than Noah, which is wrong.
- Option B: \( e - 12 = 40 \) implies Evan got 12 more than Noah, wrong.
- Option C: \( 40 - 12 = e \) is the same as \( e = 40 - 12 \), but the question is about the equation representing the situation. The situation is Evan's plus 12 equals Noah's, so D is better. But if we solve for e, \( e = 40 - 12 \), but the equation representing the situation (Evan's +12 = Noah's) is \( e + 12 = 40 \). Wait, maybe I misread. Wait, "Evan got 12 fewer correct answers than Noah" means \( e = 40 - 12 \), but the equation representing the situation: Noah's is 40, Evan's is e, and Evan has 12 fewer, so \( e + 12 = 40 \) (because Evan's plus 12 equals Noah's). So the correct equation is D. But also, \( 40 - 12 = e \) is equivalent, but the options: let's re-express. If Evan has 12 fewer than Noah (40), then \( e = 40 - 12 \), which is \( 40 - 12 = e \) (option C) or \( e + 12 = 40 \) (option D, by adding 12 to both sides). Wait, maybe the problem is about which equation represents the situation. Let's think again. The situation is: Evan's correct (e) is 12 less than Noah's (40). So \( e = 40 - 12 \), which is \( 40 - 12 = e \) (option C) or \( e + 12 = 40 \) (option D, since if you add 12 to e, you get 40). Both C and D are equivalent, but maybe the problem considers the equation that shows Evan's plus 12 equals Noah's. So D is \( e + 12 = 40 \), which is correct. But also, C is \( 40 - 12 = e \). Wait, maybe I made a mistake. Let's check the options again.

Wait, the question is "Which of the equations below represents this situation?" So the situation is: Evan got 12 fewer than Noah (who got 40). So Evan's (e) + 12 = Noah's (40). So \( e + 12 = 40 \), which is option D. Alternatively, Noah's (40) - 12 = Evan's (e), which is option C. Wait, but maybe the problem considers the equation as Evan's plus 12 equals Noah's. So D is correct. But let's check the arithmetic. If e + 12 = 40, then e = 28. If 40 - 12 = e, e is also 28. So both C and D are equivalent, but maybe the problem's intended answer is D? Wait, no, let's see the options:

A. 12 + 40 = e → e = 52 (Evan got more, wrong)

B. e - 12 = 40 → e = 52 (Evan got more, wrong)

C. 40 - 12 = e → e = 28 (correct, since 40 -12 is 28, which is 12 less than 40)

D. e + 12 = 40 → e = 28 (also correct, since 28 +12 =40)

Wait, so both C and D are correct? But that can't be. Maybe the problem has a typo, or I misinterpret. Wait, the original problem: "Evan got 12 fewer correct answers than Noah. Noah got 40 questions right. How many answers did Evan get right on the math test? Which of the equations below represents this situation?"

So the situation is: Evan's correct = Noah's correct - 12. So \( e = 40 - 12 \), which is \( 40 - 12 = e \) (option C) or \( e + 12 = 40 \) (option D, by adding 12 to both sides). So both are equivalent. But maybe the problem considers the equation that shows the relationship as Evan's +12 = Noah's, so D. Or maybe the problem's intended answer is D. Wait, let's check the options again.

Wait, maybe I made a mistake. Let's re-express:

If Evan got 12 fewer than Noah, then Noah's is Evan's +12. So \( 40 = e + 12 \), which is \( e + 12 = 40 \) (option D). So that's the equation that represents Noah's score (40) is equal to Evan's score (e) plus 12. So that's the situation: Evan's plus 12 equals Noah's. So D is correct.

Answer:

D. \( e + 12 = 40 \)