Multiple-choice questions in a test are graded by adding 2 marks for each correct

response and subtracting 1 mark for each incorrect response (including no response).
Rory and Jenny answered all the multiple-choice questions, with Rory scoring 27 and
Jenny scoring 42. Rory answered 19 questions correctly.
a How many multiple-choice questions were there?
b How many more questions than Rory did Jenny answer correctly?

i don't care / know

a.Rory

(19 correct ans X 2) 38
Rory's score -27
equals (incorrect ans)11 pts deducted

therefore
19 correct + 11 incorrect = 30 questions

b.jenny
Let x= correct answers
y= incorrect answers

equations:
2x-y=42 eq1(which is the score of jenny)
x+y=30 eq2(total no. of items)

use elimination method
then:
3x=72
divided both sides by 3
x=24

substituting to eq.1
2x-y=42
2(24)-y=42
48-y=42
y=48-42
y=6
or substituting to eq.2
x+y=30
24+y=30
y=30-24
y=6

therefore
jenny got 24 correct answers and 6 incorrect answers.

Answer for Jenny bought a gallon of orange juice. The recipe for punch calls for 2 quarts of juice. How many quarts will she have left over to drink at breakfast.

Screw you!!!

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To find the answer to these questions, we need to set up a system of equations based on the given information. Let's assume that the number of multiple-choice questions is represented by 'x'.

a) We know that Rory's score is 27 and that he answered 19 questions correctly. Each correct answer earns 2 marks, so 19 correct answers give Rory 38 marks. We also know that each incorrect/no response earns -1 mark.

Let's represent the number of incorrect/no responses as 'y'. We can set up the equation:

38 - y = 27

Simplifying the equation, we get:

y = 38 - 27
y = 11

Since each incorrect/no response earns -1 mark, the 11 incorrect/no responses mean that Rory lost 11 marks. Therefore, the total number of marks obtained by Rory is:

Total marks = 38 - 11
Total marks = 27

Now, each question is worth 2 marks, so to find the number of questions:

2x = 27
x = 27 / 2
x = 13.5

Since we can't have half a question, we can conclude that there were 13 multiple-choice questions in the test.

b) To find the number of questions Jenny answered correctly, we need to use the information that Rory answered 19 questions correctly and Jenny scored 42.

Let's represent the number of questions Jenny answered correctly as 'z'. The equation can be set up as:

2z - (x - z) = 42

Simplifying the equation, we get:

2z - x + z = 42

Replacing the value of x with 13 (from part a), we have:

2z - 13 + z = 42

Combining like terms:

3z - 13 = 42

Solving for z, we get:

3z = 42 + 13
3z = 55
z = 55 / 3
z ≈ 18.33

Since we can't have fractions of questions, we can conclude that Jenny answered 18 questions correctly.

To find the number of questions Jenny answered more than Rory:

18 - 19 = -1

Jenny answered 1 question less than Rory's correct answers. Therefore, Jenny answered 1 less question correctly than Rory.