Math
posted by Roy .
find three consecutive even intergers for which the sum of the first two integers is greater than 9 more than the third integer, and the sum of the first and third integers is less than 17 more than the second integer

"find three consecutive even intergers"
Let M be the middle integer.
The three numbers are M2, M, M+2
"the sum of the first two integers is greater than 9 more than the third integer"
(M2 + M) > M+2 + 9
on solving
M > 13
"sum of the first and third integers is less than 17 more than the second integer"
M2 + M+2 < M+17
on solving
M < 17
That leaves us with two choices,
M=14, or M=16.
Check:
M=14
12+14=26 > 16+9=25 OK
12+16=28 < 14+17=31 OK
M=16
14+16=30 > 18+9=27 OK
14+18=32 < 16+17=33 OK
So there are two valid solutions,
12,14,16 or 14,16,18
Respond to this Question
Similar Questions

maths
1. If the first and third of three consecutive odd integers are added, the result is 51 less than five times the second integer. Find the third integer. 2. Write as a subtraction problem and evaluate. 15 less than 2 n, n+1, N+2, ... … 
algebra
Five times the smallest of three consecutive odd integers is ten more than twice the longest. Find the integers. The sum of three integers is one hundred twenty three more than the first number. The second number is two more than the … 
algebra
the sum of three integers is 220. The sum of the first and second integers exceeds the third by 94. The third integer is 55 less than the first. Find the three integers. 
math
What is the smallest of three consecutive integers if the sum of the smaller two integers is equal to 177 less than four times the largest? 
math
What is the smallest of three consecutive integers if the sum of the smaller two integers is equal to 177 less than four times the largest? 
math
What is the smallest of three consecutive integers if the sum of the smaller two integers is equal to 177 less than four times the largest? 
Math please help
Three consecutive odd intergers are such that the sum of the squares of the first two integers is 54 more than 20 times the third integer. Determine the three integers. 
math please help
Three consecutive odd intergers are such that the sum of the squares of the first two integers is 54 more than 20 times the third integer. Determine the three integers. Please help and show all work thank you 
Algebra
The sum of 3 integers is 194. the sum of the first and second integers exceeds the third by 80. The third integer is 45 less than the first. Find the three integers 
Math
There are three consecutive even integers such that the sum of the first two integers is four less than the third integer. What are the integers?