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How many pairs of natural numbers at (x, y) satisfy the inequality 3x + 5y < 20?
- a)4
- b)5
- c)6
- d)8
Correct answer is option 'D'. Can you explain this answer?
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How many pairs of natural numbers at (x, y) satisfy the inequality 3x ...
The inequality 3x + 5y < 100="" can="" be="" rearranged="" as="" y="" />< (100="" -="" 3x)/5.="" />
To find the number of pairs of natural numbers (x, y) that satisfy this inequality, we can substitute different values of x and find the corresponding range of y values that satisfy the inequality.
Let's start by substituting x = 1:
y < (100="" -="" />
y < />
y < />
Since y must be a natural number, the largest value of y that satisfies the inequality is 19.
Now let's substitute x = 2:
y < (100="" -="" />
y < />
y < />
Again, the largest value of y that satisfies the inequality is 18.
We can continue this process for different values of x, but we notice that the largest value of y that satisfies the inequality decreases by 1 each time the value of x increases by 1.
Therefore, we can find the number of pairs of natural numbers (x, y) that satisfy the inequality by finding the sum of the largest value of y that satisfies the inequality for each x from 1 to infinity.
The sum of the first n natural numbers can be calculated using the formula (n(n+1))/2.
So, the number of pairs of natural numbers (x, y) that satisfy the inequality 3x + 5y < 100="" />
(19(19+1))/2 = 20*19/2 = 190.
To find the number of pairs of natural numbers (x, y) that satisfy this inequality, we can substitute different values of x and find the corresponding range of y values that satisfy the inequality.
Let's start by substituting x = 1:
y < (100="" -="" />
y < />
y < />
Since y must be a natural number, the largest value of y that satisfies the inequality is 19.
Now let's substitute x = 2:
y < (100="" -="" />
y < />
y < />
Again, the largest value of y that satisfies the inequality is 18.
We can continue this process for different values of x, but we notice that the largest value of y that satisfies the inequality decreases by 1 each time the value of x increases by 1.
Therefore, we can find the number of pairs of natural numbers (x, y) that satisfy the inequality by finding the sum of the largest value of y that satisfies the inequality for each x from 1 to infinity.
The sum of the first n natural numbers can be calculated using the formula (n(n+1))/2.
So, the number of pairs of natural numbers (x, y) that satisfy the inequality 3x + 5y < 100="" />
(19(19+1))/2 = 20*19/2 = 190.
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How many pairs of natural numbers at (x, y) satisfy the inequality 3x + 5y < 20?a)4b)5c)6d)8Correct answer is option 'D'. Can you explain this answer?
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How many pairs of natural numbers at (x, y) satisfy the inequality 3x + 5y < 20?a)4b)5c)6d)8Correct answer is option 'D'. 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 pairs of natural numbers at (x, y) satisfy the inequality 3x + 5y < 20?a)4b)5c)6d)8Correct answer is option 'D'. 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 pairs of natural numbers at (x, y) satisfy the inequality 3x + 5y < 20?a)4b)5c)6d)8Correct answer is option 'D'. Can you explain this answer?.
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