SOLUTION: translate into inequality. The sum of three intergers is no more than 110. If one interger is 9 less than twice the first and the third is one fourth the first what are the interge

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Question 408161: translate into inequality. The sum of three intergers is no more than 110. If one interger is 9 less than twice the first and the third is one fourth the first what are the intergers
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of three integers is no more than 110.

let integers be: first- x, second-y and third-z

x%2By%2Bz%3C100

If one integer is 9 less than twice the first

y%2B9%3C2x

and the third is one+fourth the first

z=%281%2F4%29x

what are the integers?


x%2By%2Bz%3C100....replace y with y%2B9%3C2x.or y%3C2x-9

x%2B%282x-9%29%2Bz%3C100...replace z with z=%281%2F4%29x

x%2B%282x-9%29%2B%281%2F4%29x%3C100.......solve for x

x%2B2x-9%2B%281%2F4%29x%3C100

3x%2B%281%2F4%29x%3C100%2B9

3x%2B%281%2F4%29x%3C109.........multiply all by 4

4%2A3x%2B4%281%2F4%29x%3C4%2A109

12x%2Bx%3C436

13x%3C436

x%3C436%2F13

x%3C33.5........it could be equal to 33.4,so
x=33.4



z=8.35


check:

x%2By%2Bz%3C100
33.4%2B58.07%2B8.35%3C100
99.82%3C100