Suppose our organization does 24 deployments per year of a particular service. Suppose that 10% of them cause an average of 8 hours of downtime and another 15% of them cause an average of 2 hours of downtime. Each hour of downtime costs us $25,000.

a. How much is the downtime costing the organization annually?

b. Suppose management has set a new goal for the year of reducing the cost of our downtime to $250,000. They like the pace at which new features are delivered so they dont want to reduce the number of deployments, but they want them to be much more reliable. What change failure rates (rounded to the nearest tenth of a percent) do we need to reach in order to achieve this goal? Hint: Maintain the relative frequencies of the bigger and smaller change failure rates. In other words that the longer failures make up 40% of all failures and the shorter ones the remaining 60%.

a is straightforward enough - we multiply the num of deployments, the change failure rate accounting for 10%, the num of hours downtime, and hourly cost of downtime; and then do the same for 15%, then add both results. however, i am confused about how to solve for x and y maintaining their 40% and 60% proportions where the right side of the equation is $250,000. any help is appreciated.