Respuesta :
Answer: the system of equations are
x + y = 35
3x + 2y = 100
Step-by-step explanation:
Let x= the number of short answer questions.
Let y= the number of multiple choice questions.
Noah wants 35 questions on the exam. This means that
x + y = 35
He plans to mix short answer questions, worth 3 points, with multiple choice questions worth 2 points. This means that x short answer questions will give 3x points and y multiple choice questions will give 2y points
Since the exam is worth 100 points, then,
3x + 2y = 100 - - - - - - - -1
Substituting x = 35 - y into equation 1, it becomes
3(35 - y) + 2y = 100
105 - 3y + 2y = 100
y = 105 - 100 = 5
x = 35 - y = 35 - 5
x = 30
The system of equation telling the number of each question Noah can have on the test is [tex]x+y = 35\\3x + 2y = 100[/tex]. The value of variables evaluates to:
- 30 = x= the number of short answer questions
- 5 = y = the number of multiple choice questions
How to form mathematical expression from the given description?
You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
For this case, we are given these facts:
- Total 35 questions will be in exam
- Two type of questions are there, one being multiple choice questions, and other being short answer questions
- Total 100 points is maximum achievable points
- Each correct multiple choice question is of 2 points
- Each correct short answer question is of 2 points
Let there are:
- x= the number of short answer questions and
- y= the number of multiple choice questions
Then, we get:
[tex]x+y = 35[/tex] (as total number of question is 35)
- Maximum points 'x' short answer can gain = [tex]3\times x[/tex]
- Maximum points 'y' multiple questions can gain = [tex]2 \times x[/tex]
Thus, we get second equation as:
[tex]3x + 2y = 100[/tex] (as total maximum score = 100 points)
Therefore, the system of equation obtained for this condition is:
[tex]x+y = 35\\3x + 2y = 100[/tex]
From first equation, getting value of x in terms of y, we get:
[tex]x = 35 -y[/tex]
Putting this in second equation, we get:
[tex]3x + 2y = 100\\3(35-y) + 2y = 100\\105 -3y + 2y = 100\\105-100 = y\\y = 5[/tex]
Putting this value of y in equation for x, we get;
[tex]x = 35 -y = 35 - 5 = 30[/tex]
Thus, the system of equation telling the number of each question Noah can have on the test is [tex]x+y = 35\\3x + 2y = 100[/tex]. The value of variables evaluates to:
- 30 = x= the number of short answer questions
- 5 = y = the number of multiple choice questions
Learn more about system of linear equations here:
https://brainly.com/question/13722693
