Question

An exam worth 388 points contains 65 questions. Some questions are worth 4 points and the others are worth 8 points. How many 4 point questions are on the test?

Answer 1

Answer:

33 questions.

Step-by-step explanation:

Let x = 4 points questions.

Let y = 8 points questions.

Translating the word problem into an algebraic equation;

For the total number of questions;

$x + y = 65$ .........equation 1

For the total number of points;

$4x + 8y = 388$ ..........equation 2

Given the following data;

Total number of questions = 65

Total number of points = 333

Solving the linear equation by using the substitution method;

Making x the subject in equation 1:

$x = 65 - y$ .......equation 3

Substituting "x" into equation 2;

$4(65 - y) + 8y = 388$

Simplifying the equation, we have;

$260 - 4y + 8y = 388$

$260 + 4y = 388$

Rearranging the equation, we have;

$4y = 388 - 260$

$4y = 128$

$y = \frac {128}{4}$

y = 32 (For the 8 points question).

Substituting "y" into equation 3;

$x = 65 - 32$

x = 33 (For the 4 points question).

Therefore, the number of 4 point questions on the test are 33 questions.