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

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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.

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