Simplfy the expression

Question

The average yearly salary of a lawyer is 24 thousand less than twice that of an architect. Combined they earn 210 thousand. Find the average yearly salary of an architect and a lawyer

Answer 1

Hi! Please assume all of my work below is in thousands. First, we need to determine the salaries of both the lawyer and the architect:

1. To solve for this algebraically, we create the following equation:
2. 210 = x + (2x-24)
3. Where "x" is the salary of the architect
4. Where "(2x-24)" represents the salary of the lawyer. Remember, the salary of the lawyer is 24 thousand less than that of the architect.
5. Where the sum of "x," the salary of the architect, and "(2x-24)," the salary of the lawyer, equals to 210 thousand
6. To solve for x, we arrange the initial equation to this by combining "like terms"
7. 210 = 3x - 24
8. Then, we can move the "-24" to the left side of the equation:
9. 186 = 3x
10. Finally, we can divide both sides by 3 to solve for "x," the salary of the architect:
11. x = $62
12. Now that we know the salary of the architect, we can use the original problem to calculate the salary of the lawyer:
13. 2x - 24
14. 2(62) - 24 = $100
15. Finally, to answer the problem, we take the average of the architect's salary, $62, and the lawyer's salary, $100:
16. (62+100)/2 = $81

Answer 2

Let x = salary of architect, in thousands

Let 2x - 24 = salary of lawyer, in thousands

2x + 2x - 24 = 210 (combined salaries, in thousands)

4x - 24 = 210

4x = 210 - 24 = 186

x = 46.5, in thousands.

The architect earns $46,500 yearly

The lawyer earns $69,000 yearly

If you want to set up a system of equations with 2 variables.

Let x = the salary of the architect, in thousands.

Let y = the salary of the lawyer, in thousands.

x + y = 210

y = 2x - 24

Solving by substitution will yield the same equation as above: x = 46.5 or $46,500

Then y = 2(46,500) - 24,000 = $69,000

Regards,

Anita A.