Answer:
The average yearly salary of the architect is <u>$62,000</u> and the lawyer is <u>$100,000</u>.
Step-by-step explanation:
Given:
The average yearly salary of a lawyer is $24 thousand less than twice that of an architect.
Combined, an architect and a lawyer earn $ 210 thousand.
Now, to find the average yearly salary of an architect and a lawyer.
Let the average yearly salary of an architect be ![x.](https://tex.z-dn.net/?f=x.)
So, the average yearly salary of the lawyer = ![2x-24,000.](https://tex.z-dn.net/?f=2x-24%2C000.)
Combined, architect and lawyer earn = ![\$210,000.](https://tex.z-dn.net/?f=%5C%24210%2C000.)
Now, to get the average salary of the architect and lawyer:
![x+(2x-24000)=210000](https://tex.z-dn.net/?f=x%2B%282x-24000%29%3D210000)
![x+2x-24000=210000\\\\3x-24000=210000](https://tex.z-dn.net/?f=x%2B2x-24000%3D210000%5C%5C%5C%5C3x-24000%3D210000)
<em>Adding both sides 24000 we get:</em>
![3x=186,000\\\\Dividing\ both\ sides\ by\ 3\ we\ get:\\\\x=62000.](https://tex.z-dn.net/?f=3x%3D186%2C000%5C%5C%5C%5CDividing%5C%20both%5C%20sides%5C%20by%5C%203%5C%20we%5C%20get%3A%5C%5C%5C%5Cx%3D62000.)
<u>The average salary of architect = $62,000.</u>
Now, to get the average salary of lawyer by substituting the value of
:
![2x-24000\\\\=2(62000)-24000\\\\=124000-24000\\\\=\$100,000.](https://tex.z-dn.net/?f=2x-24000%5C%5C%5C%5C%3D2%2862000%29-24000%5C%5C%5C%5C%3D124000-24000%5C%5C%5C%5C%3D%5C%24100%2C000.)
<u>The average salary of lawyer = $100,000.</u>
Therefore, the average yearly salary of the architect is $62,000 and the lawyer is $100,000.