Answer:
Let's make each of these workers' salaries a variable. For our purposes:
x = the annual salary of the warehouse manager
y = the annual salary of the office manager
z = the annual salary of the truck driver
*Since all of our variables describe an "annual salary" in dollars, we do not have to perform unit conversions.
From the sentence, "The sum of the annual salaries of the warehouse manager and office manager is $75000," we can derive the equation:
warehouse manager + office manager = 75000
x + y = 75000
From this sentence, "The sum of the annual salary of the office manager and the truck driver is $75000," we get:
office manager + truck driver = 75000
y + z = 75000
Finally, since "The annual salaries of the warehouse manager and the truck driver total $70000," we know that:
warehouse manager + truck driver = 70000
x + z = 70000
From the above equations, we can create a system of equations to reach the solution.
x + y = 75000
y + z = 75000
x + z = 70000
Using the substitution method and basic algebra, this question is easy! Let's solve for x, the warehouse manager's salary, first:
x + z = 70000
z = 70000 - x
y + z = 75000
y + (70000 - x) = 75000
y + 70000 - x = 75000
y - x = 5000
y = 5000 + x
x + y = 75000
x + (5000 + x) = 75000
x + x + 5000 = 75000
2x + 5000 = 75000
2x = 70000
x = $35000 = warehouse manager's annual salary
Now that we have solved for one of the variables, we can substitute our answer back in to get a quicker result:
x + z = 70000
(35000) + z = 70000
z = 35000$ = truck driver's annual salary
y + z = 75000
y + (35000) = 75000
y = $40000 = office manager's salary
So, our answers would be that:
The warehouse manager's annual salary is $35000.
The office manager's annual salary is $40000.
The truck driver's annual salary is $35000.
