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How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?
- a)8
- b)12
- c)10
- d)15
Correct answer is option 'B'. Can you explain this answer?
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How many ordered pairs of natural numbers satisfy the inequality 8x + ...
The inequality 8x - 2y < 40="" can="" be="" rewritten="" as="" 4x="" -="" y="" />< />
Let's consider the possible values for x and y.
When x = 1, the inequality becomes 4(1) - y < 20,="" which="" simplifies="" to="" -y="" />< 16.="" since="" y="" is="" a="" natural="" number,="" the="" only="" possible="" value="" is="" y="" />
When x = 2, the inequality becomes 4(2) - y < 20,="" which="" simplifies="" to="" 8="" -="" y="" />< 20.="" solving="" for="" y,="" we="" get="" y="" /> -12. Since y is a natural number, the possible values for y are 1, 2, 3, ..., 11, which is a total of 11 values.
Similarly, when x = 3, we have y > -8, giving us a total of 9 possible values for y.
Continuing this pattern, we find that when x = 1, there is 1 possible value for y. When x = 2, there are 11 possible values for y. When x = 3, there are 9 possible values for y. And so on.
Therefore, the total number of ordered pairs of natural numbers that satisfy the inequality is 1 + 11 + 9 + ... = 1 + 11 + 9 + 7 + 5 + 3 + 1 = 37.
Let's consider the possible values for x and y.
When x = 1, the inequality becomes 4(1) - y < 20,="" which="" simplifies="" to="" -y="" />< 16.="" since="" y="" is="" a="" natural="" number,="" the="" only="" possible="" value="" is="" y="" />
When x = 2, the inequality becomes 4(2) - y < 20,="" which="" simplifies="" to="" 8="" -="" y="" />< 20.="" solving="" for="" y,="" we="" get="" y="" /> -12. Since y is a natural number, the possible values for y are 1, 2, 3, ..., 11, which is a total of 11 values.
Similarly, when x = 3, we have y > -8, giving us a total of 9 possible values for y.
Continuing this pattern, we find that when x = 1, there is 1 possible value for y. When x = 2, there are 11 possible values for y. When x = 3, there are 9 possible values for y. And so on.
Therefore, the total number of ordered pairs of natural numbers that satisfy the inequality is 1 + 11 + 9 + ... = 1 + 11 + 9 + 7 + 5 + 3 + 1 = 37.
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How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer?
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How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer?.
How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many ordered pairs of natural numbers satisfy the inequality 8x + 2y ≤ 24?a)8b)12c)10d)15Correct answer is option 'B'. Can you explain this answer?.
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