High School

Jose completes his math test. The test contains 25 questions worth 120 points. The questions are of multiple-choice (MCQ) and true or false types. MCQ questions are worth 4 points each, and true or false questions are worth 6 points each. How many MCQ and true or false questions did Jose answer?

A. MCQ = 15; T/F = 10
B. MCQ = 10; T/F = 15
C. MCQ = 13; T/F = 12
D. MCQ = 5; T/F = 20

Answer :

The correct option is: A. MCQ=15; T/F=10

Let's break it down step by step:

* Total points: 120 points

* Total questions: 25 questions

* MCQ questions worth 4 points each

* True or False questions worth 6 points each

Since the total points is 120, we can set up an equation to represent the situation:

4x (MCQ points) + 6y (True or False points) = 120

Where x is the number of MCQ questions and y is the number of True or False questions.

We know that the total number of questions is 25, so we can set up another equation:

x + y = 25

Now we have a system of equations:

4x + 6y = 120

x + y = 25

To solve for x and y, we can use substitution or elimination. Let's use substitution.

Rearrange the second equation to isolate y:

y = 25 - x

Now substitute this expression for y into the first equation:

4x + 6(25 - x) = 120

Expand and simplify:

4x + 150 - 6x = 120

-2x = -30

x = 15

Now that we have found x, substitute it back into one of the original equations to find y:

y = 25 - x

y = 25 - 15

y = 10

Answer: A. MCQ=15; T/F=10

Step-by-step explanation:

Given that MCQ questions are worth 4 points each, T/F questions are worth 6 points each, and that the total score is 120 points, we can use the values to create an equation.

4x + 6y = 120

x = MCQ questions

y = T/F questions

Also given that there are 25 questions in total, we can write that as an equation too.

x + y = 25

To find the values of x and y, we can use the substitution method by first rewriting x + y = 25 in terms of x, then substituting the equation into 4x + 6y =120.

x + y = 25

x = 25 – y

Substitute into first equation and simplify:

4(25 – y) + 6y = 120

100 – 4y + 6y = 120

100 + 2y = 120

2y = 20

y = 10

Since now we know the value of y, we can substitute 10 into one of the equations to get the value of x.

x + 10 = 25

x = 15

Therefore, x = 15 and y = 10, so there are 15 MCQ questions and 10 T/F questions. (A. MCQ=15; T/F=10)

Hope this helps!