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Linear Inequalities and Systems of Linear Inequalities in Two Variables 3
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Result
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Solve each problem. Choose your answer(s). Note that certain items may have more than one answer.

1. A mathematics test is composed of two parts. Part I has 30 items worth 2 points each while part II has 10 items worth 4 points each. A student should get at least 60 points in the test. Which of the following are possible values of the number of items that the student should get correctly in the two parts of the test?
25 items in part I and
10 items in part II
20 items in part I and
9 items in part II
30 items in part I and
5 items in part II
30 items in part I and
15 items in part II
15 items in part I and
15 items in part II
none of the choices
Answer:
25 items in part I and 10 items in part II;
20 items in part I and 9 items in part II;
30 items in part I and 5 items in part II;
2. An English test consists of two types of questions. It takes a student 2 min to answer a type A question and 5 min to answer a type B question. A student has to answer a minimum of 10 type A questions and a minimum of 6 type B questions. The test is good for a maximum of 100 min. Which of the following are possible values of the number of items that the student should get correctly for the two types of questions?
30 items for type A and 15 items for type B
50 items for type A and
6 items for type B
10 items for type A and
20 items for type B
40 items for type A and
10 items for type B
20 items for type A and
20 items for type B
none of the choices
Answer: none of the choices
3. A student's average in his/her two quizzes in math should be at least 85. Each of the two quizzes should be greater than or equal to 80 and less than or equal to 100. Which of the following are possible scores that he/she should get in the two quizzes to satisfy the average requirement?
80 and 85
80 and 80
90 and 85
110 and 80
100 and 90
none of the choices
Answer: 100 and 90; 90 and 85
4. Which of the following are coordinates of the vertices of the trapezoid determined by the following system of linear inequalities?
{  y≤x+1 1≤x≤3 y≥1
(1, 2)
(3, 1)
(3, 2)
(2, 3)
(3, 4)
none of the choices
Answer: (1, 2); (3, 1); (3, 4)
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