Question
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?
Answers
GPT 3.5
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.
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.
Related Questions
Write the ratio as a fraction in lowest terms of the number of residents at Adams to the number of s...
The Philadelphia Nativist Riots of 1844 began because of anger toward the city's
African America...
The Philadelphia Nativist Riots of 1844 began because of anger toward the city's
a) African Ame...
A township is in the shape of a rectangle that is 5 km long and 4 km wide. There are 2000 residents...