Question

On a 28-question test, there are 2-point questions, 4-point questions, and 5-point questions. The test is worth a total of 100 points. There are twice as many 2-point questions as 5-point questions on the test. How many 2-point questions are on the test?

Answer 1

Answer: Number of 5-point question = 4

Number of 2-point questions =8

Number of 4-point question = 16

Explanation:

Let x = Number of 5-points question.

then, Number of 2- point question = 2x

Also, Let y = Number of 4-point question.

Now, Total question : x+y+2x =28

⇒ 3x+ y =28 (i)

Total marks = 5x + 2 (2x)+4=100

⇒ 5x+4x+4y=100

⇒ 9x+4y=100 (ii)

Multiply 3 on both sides of (i), we get

9x+3y = 84 (iii)

Subtract (iii) from (ii), we get

y= 16

Put this in (i0, we get

3x+(16)=28

⇒ 3x = 12

⇒ x=4

Now, Number of 5-point question = 4

Number of 2-point questions = 2(4)=8

Number of 4-point question = 16

Step-by-step explanation: got the answer from the last person who answered and they are correct

Answer 2

Answer: Number of 5-point question = 4

Number of 2-point questions =8

Number of 4-point question = 16

Explanation:

Let x = Number of 5-points question.

then, Number of 2- point question = 2x

Also, Let y = Number of 4-point question.

Now, Total question : x+y+2x =28

⇒ 3x+ y =28 (i)

Total marks = 5x + 2 (2x)+4=100

⇒ 5x+4x+4y=100

⇒ 9x+4y=100 (ii)

Multiply 3 on both sides of (i), we get

9x+3y = 84 (iii)

Subtract (iii) from (ii), we get

y= 16

Put this in (i0, we get

3x+(16)=28

⇒ 3x = 12

⇒ x=4

Now, Number of 5-point question = 4

Number of 2-point questions = 2(4)=8

Number of 4-point question = 16