Let's assume it will take "x" months to have an equal number of junior and senior residents on the hospital staff.
After "x" months, the number of junior residents will be 8 + 1*x = 8 + x.
After "x" months, the number of senior residents will be 6 + 3*x = 6 + 3x.
To have an equal number of each type on the hospital staff, we set the two equations equal to each other:
8 + x = 6 + 3x.
Subtracting x from both sides, we get:
8 = 6 + 2x.
Subtracting 6 from both sides, we get:
2 = 2x.
Dividing both sides by 2, we get:
x = 1.
So it will take 1 month to have an equal number of junior and senior residents on the hospital staff.
After 1 month, the number of junior residents will be 8 + 1*1 = 8 + 1 = 9.
After 1 month, the number of senior residents will be 6 + 3*1 = 6 + 3 = 9.
Therefore, after 1 month, there will be 9 junior residents and 9 senior residents on the hospital staff.
A new hospital in Silvergrove starts out with 8 junior residents and 6 senior residents on its staff. Management plans to hire additional personnel at a rate of 1 junior resident per month and 3 senior residents per month. Eventually, there will be an equal number of each on the hospital staff. How long will that take? How many of each type will there be?
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