The city of Rochester received a grant for 171700 to spend on various projects. The city board of directors decides to spend the money on three types of projects: Street projects, Urban Renewal projects, and Parks. Because of the funding source for the grant, the city will be required to spend 3 times as much on street projects as the other two projects combined. How can the money be allocated? Set up an appropriate system of equations and solve using a matrix on your calculator. {Show your work as demonstrated in the lecture videos on D2L. Show your system of equations.} a) Write the solutions to the system here, using tt as the parameter, as needed. Solution: x= $_______ for Street projects ; y= $_______ for Urban Renewal projects ; and z= $_______ for projects in the Parks. b) If the board decides to spend $14000 on Park projects, how much will be spent on the other two types? $______ spent on Street projects and on $_______ spent on Urban Renewal projects. c) Suppose a minimum of $5000 must be spent in each of the 3 project areas. Which specific solution to this problem gives the largest amount of money for the Park projects? How much would be spent on each project type in this situation? $________ for Street projects, $________ for Urban Renewal projects, and $________ for projects in the Parks.

The city of Rochester received a grant for 171700 to spend on various projects. The city board of directors decides to spend the money on three types of projects: Street projects, Urban Renewal projects, and Parks. Because of the funding source for the grant, the city will be required to spend 3 times as much on street projects as the other two projects combined. How can the money be allocated? Set up an appropriate system of equations and solve using a matrix on your calculator. {Show your work as demonstrated in the lecture videos on D2L. Show your system of equations.}

a) Write the solutions to the system here, using tt as the parameter, as needed. Solution:
x= $_______ for Street projects ;
y= $_______ for Urban Renewal projects ; and
z= $_______ for projects in the Parks.


b) If the board decides to spend $14000 on Park projects, how much will be spent on the other two types?
$______ spent on Street projects and on $_______ spent on Urban Renewal projects.


c) Suppose a minimum of $5000 must be spent in each of the 3 project areas. Which specific solution to this problem gives the largest amount of money for the Park projects? How much would be spent on each project type in this situation?
$________ for Street projects, $________ for Urban Renewal projects,
and $________ for projects in the Parks.