Find four consecutive odd integers if the product of the two smaller integers is 112 less than the product of the two larger integers. @alli14344 @jiraya
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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.
11 x 13 = 143
15 x 17 = 255
255 - 143 = 112 Yippee!