Answer:
31 questions that are worth 7 points, 14 questions that are worth 2 points
Step-by-step explanation:
the variable s will stand for the number of 7 point questions, the variable t will stand for the number of two point questions.
7s + 2t = 245
s + t = 45
-------------
t = 45 - s
7s + 2(45 - s) = 245
7s + 90 - 2s = 245
5s + 90 = 245
5s = 155
s = 31
There are 31 questions that are worth 7 points.
7(31) + 2t = 245
217 + 2t = 245
2t = 28
t = 14
There are 14 questions that are worth 2 points
The total number of 7 point questions is 31 and the total number of 2 point questions is 14 and this can be determined by forming the linear equations in two variables.
Given :
An exam worth 245 points contains 45 questions some questions are worth 7 points, and others are worth 2.
Let the total number of 7 point questions be 'x' and the total number of 2 point questions be 'y'.
The linear equation that represents the total points is:
7x + 2y = 245 --- (1)
The linear equation that represents the total number of questions is:
x + y = 45
x = 45 - y --- (2)
Now, substitute the value of 'x' in the equation (1).
7(45 - y) + 2y = 245
Simplify the above equation in order to determine the value of 'y'.
315 - 7y + 2y = 245
70 = 5y
y = 14
Now, substitute the value of 'y' in the equation (2).
x = 45 - 14
x = 31
So, the total number of 7 point questions is 31 and the total number of 2 point questions is 14.
For more information, refer to the link given below:
https://brainly.com/question/13911928
