Together, two people earn $28,000. One earns $2,000 more than the other. How much is the smaller income?

To determine how much the smaller income is, consider the relationship between the two incomes based on the information provided. Let's denote the smaller income as ( x ). According to the problem, the larger income would then be ( x + 2000 ).

The total income for both individuals is given as $28,000. Therefore, we can set up the following equation to represent their combined earnings:

[ x + (x + 2000) = 28000 ]

This simplifies to:

[ 2x + 2000 = 28000 ]

Next, subtract 2000 from both sides to isolate the terms involving ( x ):

[ 2x = 28000 - 2000 ] [ 2x = 26000 ]

Now, divide both sides by 2 to solve for ( x ):

[ x = \frac{26000}{2} ] [ x = 13000 ]

Thus, the smaller income is $13,000. This makes sense in the context of the problem because if one person's income is $13,000, the other person's income—being $2,000 more—would be $15,000. Their combined income ($13,000