William, Joseph, Margaret, Frank, and Jeffrey all work for the same company. Frank has been there the longest, eleven years, and makes the most money, three times as much as Jeffrey. Margaret has been there the second longest and makes $50,000 a year. Joseph has worked there four years less than Frank and one year more than William. He makes $60,000 a year. William’s pay is twice as much as Margaret’s. Jeffrey has worked there three years less than William and his income is three-quarters of Margaret’s. How much is Frank's annual salary?
just start writing down the data.
Frank = 3*Jeff
Marg = 50
Joe = 60
Will = 2*Marg
Jeff = 3/4 Marg
Frank = 3(Jeff) = 3(3/4 Marg) = 3(3/4(50)) = 450/4 = 112.5
So, Frank makes $112,500
To find Frank's annual salary, we can use the information given.
Let's assign variables to each person's annual salary:
- William's salary = W
- Joseph's salary = J
- Margaret's salary = M
- Frank's salary = F
- Jeffrey's salary = J
Based on the information provided, we can deduce the following facts:
1. Frank has been there the longest, eleven years.
This information does not directly help us determine Frank's salary, but it establishes his seniority.
2. Frank makes three times as much as Jeffrey.
Since Jeffrey's salary is J, we can deduce that Frank's salary is 3J.
3. Margaret has been there the second longest and makes $50,000 a year.
So, M = $50,000.
4. Joseph has worked there four years less than Frank and one year more than William.
Since Joseph's salary is J and he has worked four years less than Frank, that means William has worked four years less than Frank as well. Additionally, Joseph has worked one year more than William. This information doesn't directly provide us with salary numbers, but it helps establish the timeline and relationships between the salaries.
5. Joseph makes $60,000 a year.
So, J = $60,000.
6. William’s pay is twice as much as Margaret's.
This tells us that W = 2M, and since M is already known as $50,000, we can deduce that W = 2 * $50,000 = $100,000.
7. Jeffrey has worked there three years less than William, and his income is three-quarters of Margaret's.
Since Jeffrey's salary is J, and he has worked three years less than William, we know that William has worked for three more years than Jeffrey. We're also told that Jeffrey's salary is three-quarters of Margaret's salary, so we can determine J by multiplying three-quarters of M.
Given M = $50,000, J = (3/4) * $50,000 = $37,500.
Now, let's find F, Frank's salary, using the fact that Frank makes three times as much as Jeffrey (F = 3J):
F = 3 * $37,500 = $112,500.
Therefore, Frank's annual salary is $112,500.