# The sum of two consecutive odd integers is -148, what are the two numbers?

Feb 16, 2016

-73 and -75

#### Explanation:

We are looking for two consecutive odd numbers which add up to -148. Two consecutive odd numbers are on either side of an even number, one being one less and one being one more. Therefore, the numbers we are looking for add up to the same amount as twice the even number they bracket. In mathematical terms:

${x}_{e v e n} + {x}_{e v e n} = - 148$

or
${x}_{e v e n} = - \frac{148}{2} = - 74$

adding and subtracting one from the left-hand side of the first equation doesn't change the total and if we gather the terms together we get:

$\left({x}_{e v e n} - 1\right) + \left({x}_{e v e n} + 1\right) = - 148$

which is the same as

${x}_{o \mathrm{dd} - l o w} + {x}_{o \mathrm{dd} - h i g h} = - 148$

where

${x}_{o \mathrm{dd} - l o w} = {x}_{e v e n} - 1 = - 75$

and

${x}_{o \mathrm{dd} - h i g h} = {x}_{e v e n} + 1 = - 73$