Suppose that a city operates two neighborhood schools, one in the rich neighborhood and one in the poor neighborhood. The schools are equal in size and currently have equal budgets. The city receives $10 million in federal grant money that can be used to supplement that budgets of the two schools, which are initially identifical. For each school, the average score on a standardized achievement test depends on how many dollars are allocated to the school. Letting S denote the average test score and X denote additional spending in millions of dollars, the relationships between scores and additional spending for the two schools are as follows: Spoor = 40 + Xpoor Srich = 45 + 3Xrich (a) What are the test score results for the poor neighborhood and the rich neighborhood if the city divided the grant money equally between the schools. (b) How would the city divide the grant money if its goal is to equalize the score across schools? What is the equalized score in both schools? (c) If the city's goal is to maximize its overall average test score, which equals (Spoor + Srich)/2, how should it divide the grant money? What are the test score results for the poor neighborhood and the rich neighborhood, respectively