Question

A test worth a total of 100 points contains multiple choice questions worth 3 points each and essay questions worth 11 points each. There are 20 questions on the test. Use the graphing method to determine how many questions there are of each type.
A) 3 essay and 17 multiple choice
B) 5 essay and 15 multiple choice
C) 6 essay and 14 multiple choice
D) 10 essay and 10 multiple choice

Answer 1

The correct answer is B

Answer 2

Answer:

Test contains 15 multiple choice and 5 essay .

Option (B) is correct .

Step-by-step explanation:

Let us assume that the multiple choice questions be x.

Let us assume that the essay questions be y.

As given

A test worth a total of 100 points contains multiple choice questions worth 3 points each and essay questions worth 11 points each.

Than the equations becomes

3x + 11y = 100

There are 20 questions on the test.

Than the equations becomes

x + y = 20

The two equations are

3x + 11y = 100 and  x + y = 20

Multiply  x + y = 20  by 3 and subtracted from 3x + 11y = 100

3x - 3x + 11y - 3y = 100 - 60

8y = 40

$y = \frac{40}{8}$

y =  5

put in the equation x + y = 20

x + 5 = 20

x = 20 - 5

x = 15

Therefore test contains 15 multiple choice and 5 essay .