You are trying to design a tax system that will simultaneously achieve both of the following goals: 1) two people with the same total income would pay taxes of the same amount, and 2) a high-income person would pay a higher fraction of income in taxes than a low-income person. which of the following tax systems could achieve both goals?

A progressive tax

Explanation: A progressive tax has a direct relationship with the income earned, that is, it increases as the income increases. The tax rate applied to each income level varies such that low-income earners pay less than high-income earners but people who earn the same income pay the same amount.

Other types of  taxes are proportional tax which taxes all income levels equally and regressive tax which translates into higher taxes for low-income earners.

productive most commonly means: achieving or producing a significant amount or result.

explanation:

productive can also mean:

these depend on how the word productive is used. most likely productive will mean   achieving or producing a significant amount or result.