Mr Kevin was sitting for his driving theory test. In the first hour, he had completed 1/3 of the questions. By the next hour, he answered another 14 questions. The ratio of the questions answered to the ratio of the questions not answered became 4:1. How many questions were there in the test?

Question

Mr Kevin was sitting for his driving theory test. In the first hour, he had completed 1/3 of the questions. By the next hour, he answered another 14 questions. The ratio of the questions answered to the ratio of the questions not answered became 4:1. How many questions were there in the test?

Answer 1

If there were x questions, then

1/3 x + 14 questions were answered.
So 2/3 x - 14 were left unanswered
1/3 x + 14 = 4(2/3 x - 14)
now just solve for x

Answer 2

To solve this problem, we can use algebraic equations based on the given information. Let's denote the total number of questions in the test as "x".

In the first hour, Mr. Kevin completed 1/3 of the questions, which is (1/3)*x = x/3.

By the next hour, he answered another 14 questions, so the total number of questions answered is x/3 + 14.

According to the given information, the ratio of questions answered to questions not answered is 4:1. In other words, (x/3 + 14)/(x - x/3 - 14) = 4/1.

Simplifying this equation:

(x/3 + 14)/(2x/3 - 14) = 4/1
Cross-multiplying:

(x/3 + 14) * 1 = (2x/3 - 14) * 4
Simplifying further:

(x + 42) = (8x/3 - 56)
Multiplying by 3 to eliminate the fraction:

3(x + 42) = 8x - 168
3x + 126 = 8x - 168
126 + 168 = 8x - 3x
294 = 5x
x = 294/5
x = 58.8

Since we can't have a fraction of a question, we need to round up the answer to the nearest whole number. Therefore, there were approximately 59 questions in the test.

Answer 3

Let's assume the total number of questions in the driving theory test is represented by "x".

In the first hour, Mr Kevin answered 1/3 of the questions, which is (1/3)*x = x/3 questions.

By the second hour, he answered another 14 questions, so the total number of questions he answered by then is x/3 + 14.

The ratio of the questions answered to the questions not answered is 4:1. So, we can set up the equation:

(x/3 + 14) / (x - (x/3 + 14)) = 4/1

Now, let's simplify the equation:

(x/3 + 14) / ((2x/3) - 14) = 4/1

Cross-multiplying, we have:

(x/3 + 14) * 1 = 4 * ((2x/3) - 14)

(x/3 + 14) = 4 * (2x/3 - 14)

Expanding the right side, we get:

(x/3 + 14) = (8x/3 - 56)

Now, let's simplify and solve for x:

x + 42 = 8x - 168

7x = 210

x = 30

Therefore, there were 30 questions in the driving theory test.