In order to make a specific shade of green paint, a painter mixes 1\frac{1}{2}1 2 1 1 1 2quarts of blue paint, 2 cups of green paint, and \frac{1}{2} 2 1 1 2 gallon of white paint. How many cups of each color are needed to make 100 cups of this shade of green paint?

Browning labs is testing a new growth inhibitor for a certain type of bacteria. the bacteria naturally grows exponentially each hour at a rate of 6.2%. the researchers know that the inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. the sample currently contains 100 bacteria.the container holding the sample can hold only 300 bacteria, after which the sample will no longer grow. however, the researchers are increasing the size of the container at a constant rate allowing the container to hold 100 more bacteria each hour. they would like to determine the possible number of bacteria in the container over time.create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.