   SEARCH HOME Math Central Quandaries & Queries  Question from Pat: For 3 consecutive odd integers, twice the first integer, plus 5 more than the second integer, plus three less than four times the third integer equals -85. Find the 3 consecutive odd integers. Hi Pat,

An odd integer is one more than an even integer so for any integer n, 2n + 1 is an odd integer. I am going to let this odd integer be the middle of the three consecutive odd integers you want so the smallest is 2 less than 2n + 1 and the largest is 2 more than 2n + 1. Thus the three consecutive odd integers are

2n - 1, 2n + 1 and 2n + 3.

Now read the question carefully. You are to add three integers and get a sum of -85. The three integers to add are

twice the first integer: 2(2n - 1)

5 more than the second integer: 2n + 1 + 5

3 less than 4 times the third integer: you can do that

The sum of these three terms is -85 and this gives an equation you can solve for n. Once you know n you can find the three consecutive odd integers.

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.