Final answer:
The wife earns $10,000. We find this by setting up a system of equations representing their combined income and the husband's income relative to the wife's. Option a), h + w = $75,000, h = 5w + $15,000, correctly models the situation where h is the husband's earnings and w is the wife's earnings.
Step-by-step explanation:
To solve the question of how much the wife earns, we need to set up a system of equations based on the information provided. The total combined income of the couple is $75,000, and the husband earns $15,000 more than five times what his wife earns. We can represent the amount the husband earns as h and the amount the wife earns as w. We then have two equations:
- h + w = $75,000 (The total combined income)
- h = 5w + $15,000 (The husband earns $15,000 more than five times the wife's earnings)
Now we need to substitute the expression for h from the second equation into the first equation.
- Replace h in the first equation with the expression from the second equation: (5w + $15,000) + w = $75,000.
- Simplify the equation: 6w + $15,000 = $75,000.
- Subtract $15,000 from both sides: 6w = $75,000 - $15,000.
- Simplify: 6w = $60,000.
- Divide both sides by 6: w = $10,000.
The wife earns $10,000.
Option a) h + w = $75,000, h = 5w + $15,000 is the correct representation of the problem's equations.