Let x = multiple choice, y = true/false, z = essay
(i)
where: x + y + z = 35
We need to solve for y first, in order to know how many essay questions there are, since that is our base.
y + 2y + 4y = 35
(ii)
Now to solve:
y + 2y + 4y = 35
7y = 35
[tex]\frac{7y}{y} = \frac{35}{7}[/tex]
y = 5
Therefore, there are 5 essay questions, 10 multiple choice questions, and 20 true/false questions.
10 + 5 + 20 = 35
The equation of the system will be x + y + z = 35 and the number of each type of question should the instructor put on the test will be 5.
A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
An instructor wants to create a test that has true-false questions, multiple-choice questions, and essay questions.
Let x be the number of essay questions.
Let y be the number of multiple-choice questions.
Let z be the number of true-false questions.
He wants the test to have 35 questions, with twice as many multiple-choice questions as essay questions and with twice as many true-false questions as multiple-choice questions.
x = 2y
z = 4y
1. Then the equation of the system will be
x + y + z = 35
Then we have
2. Then the number of each type of question should the instructor put on the test will be
y + 2y + 4y = 35
y = 5
More about the linear system link is given below.
https://brainly.com/question/20379472
