The sum of three consecutive integers is 12 less than 4 times the middle integer

Step-by-step explanation:

We can set up the following equation with the information given:

, where is the middle integer.

Solving, we get:

.

The test contains 10 three-point questions and 14 five-point questions.

Step-by-step explanation:

Let x represent the number of 3-point questions.

Let y represent the number of 5-point questions.

The maths test consists of 24 questions. This means that

x + y = 24

Each question is worth either 3 points or 5 and the test is worth 100 points. This means that

3x + 5y = 100 - - - - - - - - - - -1

Substituting x = 24 - y into equation 1, it becomes

3(24 - y) + 5y = 100

72 - 3y + 5y = 100

- 3y + 5y = 100 - 72

2y = 28

y = 28/2 = 14

Substituting y = 14 into x = 24 - y , it becomes

x = 24 - 14 = 10