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

33 questions.

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.