On a test, a student scores +4 points for each correct answer and Â- 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.
