See the attached file.
Must show all work step by step and explain thoroughly.
Per Capita Income
This exercise deals with converting word problems into algebraic expressions. We will go through the wording and convert it to algebra.
"In 2004, the average of the per capita (per person) incomes for Massachusetts and Maine was $36,500."
First let use create variable to represent Massachusetts and Maine per capita incomes.
M = Massachussetts
X = Maine
Then, because it state that the per capita incomes was 36,500 for both states we write:
Mass. + Maine = 36,500
M + X = 36,500 (1)
Another important fact is given in the problem: "The per capita income in Mass. exceeded the per capita income in Maine by $11,000"
Exceed means to be more than. Translating this to algebra, this means:
M = 11,000 + X (2)
Thus, we have set a system of equations.
To solve for the variables M and X (per capita of Mass. and Maine), we substitute equation (2) into equation (1).
(11,000 + X) + X = 36,500 ...
The solution discusses per capita income and CEO salary.