Algebra

you are about to take a test that contain questions of type A worth 4 points and of type B worth 7 points. You must answer at least 5 of type A and 3 of type B, but time restricts answering more than 10 of either type. In total, you can answer no more than 18. How many of each type of question can you answer, assuming all of your answers are correct, to maximize your score? What is the maximum score?

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. You want to answer as many of type B as possible because they're worth the most points.
    10*7 = 70
    That leaves eight questions of type A that you can answer.
    8*4 = 32

    70 + 32 = 102

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  2. let the number of questions answered from part A be x
    let the number of questions answered from part B be y

    we have 3 main conditions:
    x ≤ 10
    y ≤ 10 and
    x+y ≤ 18

    also we have x>5 and y>3

    sketch this on a graph and any point with integer coordinates in the first quadrant that satisfies these conditions would be a possible "test".

    Then Marks = 4x + 7y

    this can be represented by a straight line with slope -4/7.
    we want this line to be as far away from the origin as possible, (highest mark), but still be in contact with the region we have defined.

    notice the slope of x+y=18 is -1 which is 45º to the left, while a slope of -4/7 is a line not yet 45º

    so marks=4x+7y would still touch our region at the point (10,18), namely the intersection of the boundaries x+y=18 and y=10

    so you should answer 8 questions form part A and 10 questions from part B
    for a total score of 102

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    (08.02)The scores of several classmates on a science test are shown below: 85 points 91 points 76 points 80 points 83 points 89 points 94 points 75 points 84 points 94 points What is the median score for these students? 83 points

  2. Math

    A 100 point test contains a total of 20 questions. The multiple choice questions are worth 3 points each and the short response answer questions are worth 8 pints each. Write a system of linear equations that represents this

  3. Algebra

    A test has 15 questions worth 100 points in total. The test consists of multiple choice questions, which are 4 points each, and open-response questions, which are worth 12 points each. How many multiple choice questions are on the

  4. Statistics

    In your biology class, your final grade is based on several things: a lab score, score on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 25% of

  1. math

    On a 28-question test, there are 2-point questions, 4-point questions, and 5-point questions. The test is worth a total of 100 points. There are twice as many 2-point questions as 5-point questions on the test. How many 2-point

  2. Math

    Write a proportion to find how many points x a student needs to score on a test worth 50 points to get a test score of 40%.

  3. math

    on a 10 question quiz you correctly answer four one point questions and five two point questions. you earn 87.5% of the possible points on the quiz. a. how many possible points is the quiz worth b. how many questions did you miss

  4. math

    Your teacher is giving you a test worth 100 points containing 40 questions. There are two-point and four-point questions on the test. How many of each type of question are on the test? How would you set this up?

  1. business

    please help Which of the following is not a travel, hospitality, and tourism career? Chef Pilot Curator Truck Driver Question 3(Multiple Choice Worth 1 points) What is true about semi truck drivers? They often attend vocational

  2. Math

    There are 40 questions on a class test. Six points are given for each correct answer and three points are deducted for each wrong answer. Find the number of correct answers for a test score of 105.

  3. Strayer

    A certain test is worth 125 points. How many points (rounded to the nearest point) are needed to obtain a score of 85%?

  4. mathematics

    Jake correctly answered 15 out of 25 questions in Test 1 and 18 out of 25 questions on test 2. On Test 3 he missed 5 out of 27 questions. Which test had the best score? A) Test 2 and Test 3 B) Test 2 C) Test 3 D) Test 1 ??

View more similar questions or ask a new question.