Find two positive integers such that the sum of the first number and four times the second number is 1000 and the product of the two numbers is as large as possible. Show all of your work.

Q: Find three consecutive even intergers such that the product of two smaller numbers is the same as…

A: Let the consecutive even integers be  x, x+2,x+4, where x  is even , then we use the given condition…

Q: Divide 120 into two parts so that product of one and the square of the other is maximum Find the…

A: Let the two parts be x and y.x+y = 120⇒ y = 120-x  --------------(1)  Maximize the product of "one…

Q: Find two positive numbers, x and y, whose sum is 100 and whose product is as large as possible.

A: Let the two positive numbers are x and y. Now, Their sum is 100. That is,          x+y=100⇒y=100-x

Q: Find the two positive integers whose sum is 16 and the sum of whose square is minimum

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Q: Find three consecutive even integers such that the sum of the squares of the first two is four less…

A: Let the three consecutive even integers are n , n+2, n+4

Q: What two positive real numbers whose product is 72 have the smallest possible sum?

A: let two real numbers are a and b then according to question ab=72..........(I) let sum is S then…

Q: Find two positive integers such that the sum of the first and five times the second number is 2000…

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Q: Find two nonnegative numbers whose sum is 9 and so that the product of one number and the square of…

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Q: The digit of positive integer, having three digits are in AP. And are their sum is 15. The number…

A: given that three digits sum is 15number obtained by reversing the digits is 594 less than the…

Q: Find three consecutive odd integers such that their sum decreased by the second equals 50.

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Q: Find two non negative integers whose sum is 25 and whose product with the square of the other number…

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Q: Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible.…

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Q: Verify that for any three consecutive integers, the sum of the smallest and largest is equal to…

A: Given: Three consecutive integers.

Q: Find two positive numbers such that the sum of twice the first number and three times the second…

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Q: Find the minimum sum of two positive numbers (not necessarily integers) whose product is 200.

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Q: Find two positive numbers such that the sum of twice the first number and three times the second…

A: Let one number be 'x' and other number be 'y'.  Given that sum of twice of one number and thrice of…

Q: Find the smaller of two consecutive integers such that twice the smaller exceeds the larger by 10.

A: We can solve the problem by taking the smaller one as x and the larger one as x+1.

Q: Find two non-negative numbers such that the sum of two times the first and three times the second s…

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Q: Find the numbers whose sum is 20, if the product of one by the cube of the other is to be maximum.

A: This question is about sum and product of 2 numbers & to find maximum.

Q: Find three consecutive odd intergers such that the product of the two larger numbers is 18more than…

A: To form the equation satisfied by the required integers  and therby solve for them

Q: Find three consecutive positive odd integers such that the square of the first is 9 more than 6…

A: Given : The square of the first is 9 more than 6 times the sum of the second and third

Q: Find two positive numbers such that the sum of twice the first number and three times the second…

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Q: Find two positive numbers, x and y, whose product is 100 and whose sum is as small as possible.

A: Suppose x and y be the positive numbers whose product is 100 So, xy=100 Then, y=100x…

Q: Find two positive real numbers such that they sum to 108 and the product of the first times the…

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Q: Find three positive numbers whose sum is 24 and such that their product is as large as possible.

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Q: . Find two positive integers such that the sum of the first number and four times the second number…

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Q: . Find the three positive numbers whose sum is 48 and whose product is as large as possible.…

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Q: Find three positive numbers that sum to 150 with the greatest possibleproduct of the three.

A: Given: we to find three numbers that sum to 150

Q: Find two nonnegative numbers such that the sum of first number and 3 times the second number is 1200…

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Q: Find three consecutive odd integers such that the product of the first two is 52 more than the third…

A: Let the three consecutive odd integers are  n-2, n and n+2 So as per question, product of first two…

Q: Find two positive integers such that the sum of the firstnumber and four times the second number is…

A: Let the first number be x. Let the second number be y.   Given: x+4y=1000x=1000-4y   Determine the…

Q: Find two nonnegative numbers such that the sum of first number and 4 times the second number is 1600…

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Q: Find two consecutive integers such that tn more than twice the smaller is seven less than three…

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Q: Is a product of two positive decimals each less than 1 always less than each of the decimals?

A: To state the give statement is true or false.

Q: Find the two numbers whose sum is a. If the product of the square of one by the cube of the other is…

A: Let us consider the function f(x)  To maximize the function  Differentiate the function with…

Q: find three consecutive odd integers such that the sum of the first and the second is sixteen more…

A: Given:The three consecutive integers are odd numbers.The sum of the first two consecutive odd number…

Q: Find the two consecutive positive integers such that the square of the first is decreased by 17…

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Q: Find two positive numbers x and y , whose product is 900 and whose sum is as small as possible

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Q: Determine what will be the three positive numbers that its product is 27 and its sum is as small as…

A: We will find the three numbers satisfying the given conditions.

Q: Find two integers whose sum is 140 and whose product is as large as possible.

A: Topic=Algebra Two integers are 70 and 70.

Q: Find two concecutive odd integers such that when the smaller is added to twice the larger, the…

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Q: What two positive real numbers whose product is 19 have the smallest possible​ sum?

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Q: The product of two positive numbers is 185. The smallest possible sum of those number is

A: Since,The prime factorization of 165 is 1Q5 =1X5 X37=5X37 ----1 From 1 it is clear that the two…

Q: Find the three consecutive integers such that that product of the first and third is one less than…

A: Take three consecutive integer as below :n-1, n , n+1

Q: The width of a rectangular area is 10 m and its height is (2x – 4) m. If the area is less than 80…

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Q: Divide the number 120 into two parts such that the product of one part and the square of the other…

A: To divide the number 120 into two parts such that the product of one part and the square of the…

Q: Find two positive real numbers whose sum is 40 and whose product is a maximum.

A: A function f(x) is said to have a maximum value at a point c when the first derivative of the…

Q: Find two positive real numbers whose product is a maximum. The sum of the first and three times the…

A: Here, we need to find two positive real numbers whose product is a maximum. The sum of the first and…

Q: Find two positive integers such that the sum of the first number and four times the second number is…

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Q: Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.