What are the important variables in the problem below?
a test is worth 60 points. multiple-choice questions are worth 2 points, and
short-answer questions are worth 5 points. if the test has 15 questions, how
many multiple-choice questions are there?
o
a. for test, q for questions
o
b. m for multiple choice, sfor short answer
o
c. p for points, m for multiple choice
o
d. sfor short answer, t for test

The important variables in the problem are:

B. for multiple choice, for short answer

The number of multiple choice questions = 5

Step-by-step explanation:

Given:

Total number of questions = 15

Total points for the test = 60

Multiple choice question carries = 2 points

Short-answer question carries = 5 points

To determine the number of multiple choice questions in the test.

Solution:

Let represent the number of multiple choice questions.

If 1 multiple choice question carries = 2 points

The, questions will carry = points

Let represent the number of short-answer questions.

If 1 short-answe question carries = 5 points

The, questions will carry = points

Total questions can be given as :

Total points can be given as :

Thus, we can model two equations form the given data.

A)     [Number of questions]

B)  [ Total points]

Thus, and are important variables in the problem.

Rearranging equation A, to solve for in terms of

Subtracting both sides by

Substituting value of we got from A into equation B.

Using distribution.

Simplifying.

Subtracting both sides by 75.

Dividing both sides by -3.

∴

Thus, number of multiple choice questions = 5

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form