Final answer:
For part a, the wife could have earned between 810 and approximately 1156.19 dollars. For part b, the husband could have earned between approximately 343.81 and 1156.19 dollars, based on the given total earnings constraint of 1000 to 1500 dollars and the wage gap ratio.
Explanation:
Given that for every 81 dollars that women earn, men earn 100 dollars, we can set up a ratio to calculate the potential earnings of a husband and wife. To find the range of possible earnings for each, we will use the combined total earnings constraint of between 1000 and 1500 dollars.
Part a: Potential Earnings for the Wife
If the wife earns 81 dollars for every 100 dollars the husband earns, her maximum possible earning, when the husband earns 1000 dollars (the minimum based on the given constraint for combined earnings), would be 81/100 * 1000 = 810 dollars. Similarly, her minimum possible earning, when the husband earns 1500 dollars (the maximum based on the given constraint for combined earnings), would be 81/100 * (1500 - 81) = approximately 1156.19 dollars (using the upper limit and subtracting the wife's equivalent of 1 dollar to avoid double-counting).
Part b: Potential Earnings for the Husband
The husband's minimum possible earning is when the wife earns 1500 dollars, which is 100/81 * (81 - 1500/81) = approximately 343.81 dollars (using the lower limit and the wife's equivalent of 1 dollar). His maximum earnings would be 1500 dollars, assuming the wife earned nothing, which is not possible given the constraints. Hence, his maximum earning, when the wife earns the minimum calculated above, would be 1500 - 343.81 = approximately 1156.19 dollars.