Final answer:
The smaller income earned by one of the two people is $13,000, calculated by setting up a system of equations and solving for the unknown value.
Step-by-step explanation:
To determine the smaller income between the two people who earned a combined total of $28,000, where one earned $2,000 more than the other, we can set up a system of equations. Let's call the smaller income x, then the larger income would be x + $2,000. The sum of their incomes is $28,000. So, we can write:
x + (x + $2,000) = $28,000
Combining like terms, we get:
2x + $2,000 = $28,000
Subtracting $2,000 from both sides, we have:
2x = $26,000
Dividing both sides by 2 gives us:
x = $13,000
Therefore, the smaller income is $13,000.