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

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

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