Question

31 32 33 34 35 36 37 38 39 40

Answer 1

Answer:

The correct answer is: The test had 10 4-point questions and 30 3-point questions.

Step-by-step explanation:

Let t be the number of 3-point questions on the test

and

f be the number of 4-point questions on the test

Then,

According to the given statement that the test had 40 problems

$t+f = 40$  Eqn 1

And

According to given statement that the total points are 130

$3t+4f = 130$  Eqn 2

These equations form a system of linear equations in two variables.

Elimination method or substitution method can be used to solve the system.

So, from equation 1:

$t+f = 40\\t = 40-f$

Putting t = 40-f in equation 2

$3(40-f) +4f = 130\\120-3f+4f = 130$

Subtracting 120 from both sides

$120-3f+4f-120 = 130-120\\f = 10$

Putting f = 10 in equation 1

$t+10 = 40$

Subtracting 10 from both sides

$t+10-10 = 40-10\\t = 30$

Hence,

Number of 3-point questions = t = 30

Number of 4-point questions = f = 10

So,

The correct answer is: The test had 10 4-point questions and 30 3-point questions.