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Word problems

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Word problems

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On a test, a student scores +4 points for each correct answer and ­- 2 points for each incorrect answer. Jack attempted 20 questions and found that his score would have been 44 if he had got two more questions correct. How many questions did Jack get incorrect?
A. 6
B. 8
C. 10
D. 12
E. 14
OA is b
what is the mathematical approach to use here in order to get the correct answer?

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Roland2rule wrote:
On a test, a student scores +4 points for each correct answer and ­- 2 points for each incorrect answer. Jack attempted 20 questions and found that his score would have been 44 if he had got two more questions correct. How many questions did Jack get incorrect?
A. 6
B. 8
C. 10
D. 12
E. 14
OA is b
what is the mathematical approach to use here in order to get the correct answer?
Not a bad one to back solve. Test C. Say Jack answered 10 questions incorrectly. This means he answered 10 questions correctly. Had he answer two more questions correctly, we'd have answered 12 questions correctly and 8 questions incorrectly, for a score of 12*4 + 8*(-2) = 48 - 16 = 32. But we know he should have received a 44. C is too small, so he had to have answered fewer questions incorrectly. Eliminate C, D, and E.

Test either A or B. (Note that there's no reason to test both. If whatever you try works, it's the answer. If it doesn't the answer is the other one.)

Let's try B. If he answered 8 questions incorrectly, he answered 12 questions correctly. Had he answered two more questions correctly, he'd have answered 14 questions correctly and 6 questions incorrectly, for a score of 14*4 + 6(-2) = 56 - 12 = 44. There's our answer. B is correct.

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Post
Quote:
On a test, a student scores +4 points for each correct answer and ­- 2 points for each incorrect answer. Jack attempted 20 questions and found that his score would have been 44 if he had got two more questions correct. How many questions did Jack get incorrect?
A. 6
B. 8
C. 10
D. 12
E. 14
OA is b
what is the mathematical approach to use here in order to get the correct answer?
Hi Roland2rule,
Let's take a look at your question and solve it algebraically.

Jack attempted 20 questions in total.
For each correct answer he got +4 points and for each incorrect answer he got -2 points.

The question states that Jack would have scored 44 points if he had got two more questions correct.

Let Jack solved x questions correctly and (20 - x) questions incorrectly.
If he got 2 more questions correct then he would have scored 44 points.
It means that if correct questions are (x + 2) and incorrect questions are [20 - (x + 2)] then Jack's score would have 44.
We can write it as:

$$4\left(x+2\right)-2\left[20-\left(x+2\right)\right]=44$$
$$4\left(x+2\right)-2\left[20-x-2\right]=44$$
$$4\left(x+2\right)-2\left(18-x\right)=44$$
$$4x+8-36+2x=44$$
$$6x-28=44$$
$$6x=44+28$$
$$6x=72$$
$$x=\frac{72}{6}$$
$$x=12$$

x represents the number of correct questions, we need to find the number of questions Jack get incorrect.
Number of incorrect questions = 20 - 12 = 8

Therefore, Option B is correct answer.

Hope it helps.
I am available if you'd like any follow up.

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