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What is four odd integers if the product of the two smaller integers is 112 less than the product of the two larger integers?
Wiki User
∙ 12y ago
We began by assuming that the 4 odd integers are consecutive, and everything
worked just fine. So, although there may well be more than one correct answer to
the question as it's stated, we have a hunch they're supposed to be consecutive,
and that detail was accidentally left out of the question.
Call the 4 consecutive odd integers (2x - 3), (2x - 1), (2x + 1), and (2x + 3).
Product of the two larger ones = (4x2 + 8x + 3)
Product of the two smaller ones = (4x2 - 8x + 3)
Smaller product + 112 = larger product . . . . . (4x2 - 8x + 3) + 112 = (4x2 + 8x + 3)
Eliminate parentheses . . . . . 4x2 - 8x + 115 = 4x2 + 8x + 3
Subtract (4x2 + 3) from each side . . . . . -8x + 112 = 8x
Add 8x to each side . . . . . 112 = 16x
Divide each side by 16 . . . . . x = 7
The consecutive odd integers are: 11, 13, 15, and 17.
Check:
11 x 13 = 143
15 x 17 = 255
255 - 143 = 112 Yippee!
Wiki User
∙ 12y ago
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Find four consecutive odd integers if the product of the two smaller integers is 112 less than the product of the two large integers?
The numbers are 11, 13, 15 and 17.
Find 4 consecutive integers even integers where the product of the smaller number is 72 less than the product of the two larger numbers?
The four even integers are 6, 8, 10, 12. 6 x 8 = 48 10 x 12 = 120 120 - 48 = 72
Find four consecutive odd integers if the product of the two smaller integers is 112 less than the product of the two larger integers?
11,13,15,17solve this: n(n-2)=(n-4)(n-6)+112n is the highest of the four.solving, you get:n^2 -2n=n^2-10n+1368n=136n=136/8n=17so, the four are: 11, 13, 15, 17.
Find two consecutive even integers such that the smaller added to four times the larger gives a sum of 58?
10,12
When the smaller of two consecutive integers is added to four times the larger the result is 59?
Let the smaller be n, then the larger is n+1; and: n + 4(n+1) = 59 → n + 4n + 4 = 59 → 5n = 55 → n = 11 → the two consecutive integers are 11 and 12.
Find 4 consecutive even integers where the two smaller numbers is 56 less than the product of two larger numbers?
The four even integers are 4, 6, 8, and 10. 10 x 8 = 80 6 x 4 = 24 80 - 24 = 56
If the sum of two integers is -5 Their product is four What are the integers?
-4 and -1
The larger of two numbers is 8 more than 4 times the smaller if the larger number is increased by four times the smaller the result is 40?
The larger of two numbers is 8 more than 4 times the smaller if the larger number is increased by four times the smaller the result is 40. From this statement, we can calculate the values of the numbers where you get the value of the larger number to be 24 and that of the smaller number to be 4.
What is the link between the product of any four consecutive positive integers and some square numbers?
The product of four consecutive integers is always one less than a perfect square. The product of four consecutive integers starting with n will be one less than the square of n2 + 3n + 1
Is three-fifths is larger or smaller than four-twelfths?
It is larger.
What is the sign of the product when you multiply four integers?
The sign of the product of four integers depends on the signs of the individual integers. There are 4 cases: 1) When all 4 integers share the same sign and all are non-zero (either all are positive or all are negative), the product is positive. 2) When 3 of the 4 integers share the same sign and all are non-zero (3 are positive and 1 is negative; or 3 are negative and 1 is positive), the product is negative. 3) When 2 of the integers are positive non-zero and the other 2 of the integers are negative non-zero, the product is positive. 4) If even one of the integers is zero, the product is zero (no sign - it is neither positive nor negative).
Find two consecutive even integers such that the smaller added to four times the larger gives a sum of 28?
x = smallest x+2 = largest x +4(x+2) = 28 5x +8 = 28 5x = 20 x =4 (smaller) X+2 = 6 (larger)
