In a 3 hour examination of 350 questions, there are 50 mathematics problems. If twice as much time should be allowed for each problem as for each of the other questions, how many minutes should be spent on the mathematical problems?
not just and answer please
A.45
B.52
C.60
D.68
E.72
Assuming you mean to exhaust the time allotted, figure the time used on non-math questions as x, so
50*2x + 300x = 180
400x = 180
x = 9/20
50*18/20 = 45
So, (A)
To approach this problem, we need to determine how much time is allotted for each type of question and then calculate the total time for the mathematics problems.
Let's start by calculating the time for each type of question. We know that the examination lasts for 3 hours, which is equivalent to 180 minutes.
If we divide the 350 questions into two categories (mathematics problems and other questions), we can set up the following equation:
50x + (350 - 50)y = 180
Where x represents the time for each mathematics problem and y represents the time for each of the other questions.
We also know that twice as much time should be allowed for mathematics problems as for the other questions. So, we have:
x = 2y
Now, we can substitute the value of x in terms of y into our equation:
50(2y) + (350 - 50)y = 180
Simplifying the equation gives us:
100y + 350y - 50y = 180
Combine like terms:
400y = 180
Now, solve for y:
y = 180/400
Simplify:
y = 9/20
Since y represents the time for each of the other questions, we can multiply it by 60 to convert it to minutes:
y (minutes) = (9/20) * 60
Simplifying gives us:
y (minutes) = 27
Now, to find the time for each mathematics problem, we can substitute the value of y into our equation for x:
x = 2y
x = 2 * 27
x = 54
So, the time allotted to each mathematics problem is 54 minutes.
Therefore, the correct answer is not provided in the options.
To solve this problem, we need to first determine how much time is allotted for each question. Since the total examination time is 3 hours (which is equal to 180 minutes), we can divide this by the total number of questions to find the time allotted per question:
180 minutes ÷ 350 questions = 0.514 minutes per question (rounded to 3 decimal places)
Now, since the other 300 questions each have the same time allotted, we can calculate the time allotted for the math problems. As mentioned in the question, math problems are given twice as much time as the other questions. Therefore, we just need to double the time allotted for each question:
0.514 minutes per question × 2 = 1.028 minutes per math problem (rounded to 3 decimal places)
Now, we need to calculate how many minutes should be spent on the mathematical problems in total. We do this by multiplying the number of math problems (50) by the time allotted per math problem:
50 math problems × 1.028 minutes per math problem = 51.4 minutes
Since the time needs to be rounded to the nearest whole number of minutes, we have:
Rounded answer = 51 minutes
So, the correct answer is 51 minutes. However, this option is not listed among the choices provided. It seems like there may be a mistake in the available answer choices, as the closest option is 52 minutes (Option B).
Therefore, the most appropriate answer choice, based on the given options, would be B.52.