Mrs. Williams created the Unit 9 Test. Some of the questions are worth 3 points and other questions are worth 2 points. The test is worth a total of 36 points. If x represents the questions worth 3 points and y represents the questions worth 2 points, use an equation that models this situation to answer the question below:Find how many questions worth 2 points Mrs. Williams will need to add if she decided to use 4 questions worth 3 points.
Question
Mrs. Williams created the Unit 9 Test. Some of the questions are worth 3 points and other questions are worth 2 points. The test is worth a total of 36 points. If x represents the questions worth 3 points and y represents the questions worth 2 points, use an equation that models this situation to answer the question below:Find how many questions worth 2 points Mrs. Williams will need to add if she decided to use 4 questions worth 3 points.
Solution
Given that the total points of the test is 36 and each question worth 3 points is represented by x and each question worth 2 points is represented by y, we can form the equation:
3x + 2y = 36
We are asked to find the number of 2-point questions (y) if there are 4 questions worth 3 points (x=4). Substituting x=4 into the equation gives:
3*4 + 2y = 36 12 + 2y = 36 2y = 36 - 12 2y = 24
To find y, we divide both sides of the equation by 2:
y = 24 / 2 y = 12
So, if Mrs. Williams decided to use 4 questions worth 3 points, she will need to add 12 questions worth 2 points.
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