Question

On a 28-question test, there are 2-point questions, 4-point questions, and 5-point questions, totaling 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?

A) 4
B) 8
C) 12
D) 16

Answer 1

By assigning variables for the number of questions of each point value and setting up equations based on the information given, we can solve for the number of 2-point questions. We find that there are 8 2-point questions on the test.

Step-by-step explanation:

To solve this problem, let us denote the number of 2-point questions as x, the number of 4-point questions as y, and the number of 5-point questions as z. According to the problem, the total number of questions is 28, and there are twice as many 2-point questions as 5-point questions. The total score of the test is 100 points.

The problem can be described by the following equations:

• x + y + z = 28 (total number of questions)
• 2x + 4y + 5z = 100 (total points of the test)
• x = 2z (twice as many 2-point questions as 5-point questions)

Let's use substitution for x = 2z in the other equations:

• 2z + y + z = 28 → y + 3z = 28
• 2(2z) + 4y + 5z = 100 → 4z + 4y + 5z = 100 → 4y + 9z = 100

From the first simplified equation, we can express y as:

y = 28 - 3z

Now, replace y in the second simplified equation:

4(28 - 3z) + 9z = 100 → 112 - 12z + 9z = 100 → -3z = -12 → z = 4

Having found z, we can determine x:

x = 2z = 2(4) = 8

Therefore, there are 8 2-point questions on the test.