Question

A married couple had a combined annual income of $49,000. The wife made $1000 more than her husband. What was each of their incomes?

a) The wife's income was $25,000.

b) The husband's income was $24,000.

c) The wife's income was $24,000.

d) The husband's income was $25,000.

Answer 1

By setting up a system of linear equations, we determine that the husband's income is $24,000, and the wife's income is $25,000.

Step-by-step explanation:

To determine the incomes of the wife and husband, we can set up a system of linear equations based on the information given. Let's define the husband's income as X and the wife's income as X + $1,000. Their combined income is $49,000, which gives us the first equation: X + (X + $1,000) = $49,000.

To solve for X, we combine like terms and subtract $1,000 from both sides: 2X + $1,000 = $49,000; 2X = $48,000; X = $24,000. Therefore, the husband's income is $24,000, and the wife's income, being $1,000 more, is $25,000.

This means that the correct answers are:

• b) The husband's income was $24,000.
• a) The wife's income was $25,000.