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?

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

a = 2 pt, b = 4 pt, c = 5 pt

a + b + c = 28

2a + 4b + 5c = 100

a = 2c

2a + 2b + 2c = 56
... substituting ... 3a + 2b = 56

4a + 8b + 10c = 200
... substituting ... 9a + 8b = 200

subtract the equations (after multiplying) to eliminate b

Answer 2

Let's denote the number of 2-point questions as x and the number of 5-point questions as y.

From the given information, we know that there are twice as many 2-point questions as 5-point questions. Therefore, we can write the equation: x = 2y.

We are also told that there are 28 questions in total on the test, so we can write another equation: x + y = 28.

To solve these two equations, we can substitute the value of x from the first equation into the second equation.

Substituting x = 2y into x + y = 28, we get:

2y + y = 28.

Combining like terms, we have:

3y = 28.

Dividing both sides by 3, we find:

y = 28 / 3.

y is not a whole number, which implies that the given information may not be accurate or there is a mistake in the question.

In conclusion, there is not a whole number answer to the question of how many 2-point questions are on the test.

Answer 3

To find the number of 2-point questions on the test, we can use algebra. Let's assume the number of 2-point questions is 'x' and the number of 5-point questions is 'y'.

Given:
Total questions = 28
Total points = 100
Number of 2-point questions = x
Number of 5-point questions = y

We know that the test is worth a total of 100 points, so we can write the equation:
2x + 4y + 5(y) = 100

Since there are twice as many 2-point questions as 5-point questions, we can write another equation:
x = 2y

From the second equation, we can substitute x in the first equation with 2y:
2(2y) + 4y + 5y = 100
4y + 4y + 5y = 100
13y = 100
y = 100 / 13

Now we can solve for y:
y ≈ 7.69

Since the number of questions cannot be a decimal, let's round up the value of y to the nearest whole number:
y ≈ 8

Now substitute this value of y back into the second equation to find x:
x = 2(8)
x = 16

Therefore, there are 16 2-point questions on the test.