Question

Penny sits for a test containing 20 questions (She answers 20 questions) She is awarded 2 marks for each correct answer and 1 mark is deducted for each incorrect answer. If Penny answers 28 marks as her final score, how many questions did she answer correctly?

Answer 1

━━━━━━━━━━━━━━━━━━━━

✤ Required Answer:

✒️ GiveN:

• Total number of questions is 20
• For every correct answer, 2 marks are awarded.
• For every incorrect answer, 1 mark is deducted.
• Marks obtained by Penny is 28

✒️ To FinD:

• Number of correct answers by Penny....?

━━━━━━━━━━━━━━━━━━━━

✤ How to solve?

We will frame some equations, that is simultaneous linear equations in two variables where we will consider the number of correct & incorrect answers be any variables. After that, we can solve it by elimination or substitution method.

━━━━━━━━━━━━━━━━━━━━

✤ Solution:

Let,

• The number of correct answers be x
• And, number of incorrect answers be y

According to condition-1),

➝ Total number of questions = 20

➝ No. of correct answers + No. of incorrect answers = 20

➝ x + y = 20 ............(1)

This is our first equation ⏫

According to condition-2),

➝ Marks obtained by Penny = 28

➝ Marks for correct answers + Marks for incorrect answers = 28

Here,

• Marks for correct answers = +2
• Marks for incorrect answers = -1

➝ +2(x) -1(y) = 28

➝ 2x - y = 28.........(2)

This is our second equation ⏫

Adding equation (1) & equation (2),

➝ x + y + 2x - y = 20 + 28

➝ 3x = 48

➝ x = 48/3

➝ x = 16

So, Number of correct answers:

• $\Large{ \underline{ \boxed{ \rm{ \red{16}}}}}$

━━━━━━━━━━━━━━━━━━━━

Answer 2

Answer:

✡ Question ✡

✏ Penny sits for a test containing 20 questions (She answers 20 questions) She is awarded 2 marks for each correct answer and 1 mark is deducted for each incorrect answer. If Penny answers 28 marks as her final score, how many questions did she answer correctly?

✡ Given ✡

⚫Total number of questions is 20

⚫For every correct answer, 2 marks are awarded.

⚫For every incorrect answer, 1 mark is deducted.

⚫Marks obtained by Penny is 28

✡️ To Find ✡

➡Number of correct answers by Penny?

✡ Solution ✡

▶Let,

⭐The number of correct answers be x

⭐And, number of incorrect answers be y

▶According to condition :- (1)

=> Total number of questions = 20

=> No. of correct answers + No. of incorrect answers = 20

=> x + y = 20 ............(1)

▶According to condition :- (2)

=> Marks obtained by Penny = 28

=> Marks for correct answers + Marks for incorrect answers = 28

Now,

➡Marks for correct answers = +2

➡Marks for incorrect answers = -1

=> +2(x) -1(y) = 28

=> 2x - y = 28.........(2)

Now we have to add equation no (1) and equation no (2) we get,

=> x + y + 2x - y = 20 + 28

=> 3x = 48

=> x = 48/3

=> x = 16✔

✍ Hence , Number of correct answers given by Penny is

$\bold{\huge{\fbox{\color{blue} {</em><em>1</em><em>6</em><em>}}}}$

Step-by-step explanation:

HOPE IT HELP YOU