Answer:
$654
Step-by-step explanation:
Let the amount of money Marlina's received for her salary be x.
We know that she spent 1/2 of her salary on rent and then $338 on her electric and water bill. So, after this, she will have:
![x-\frac{1}{2}x-338](https://tex.z-dn.net/?f=x-%5Cfrac%7B1%7D%7B2%7Dx-338)
Left of her salary.
Next, she spent one half of what was left. So, it will be one-half of the equation. Therefore, she will have spent:
![x-\frac{1}{2}x-338-\frac{1}{2}(x-\frac{1}{2}x-338)](https://tex.z-dn.net/?f=x-%5Cfrac%7B1%7D%7B2%7Dx-338-%5Cfrac%7B1%7D%7B2%7D%28x-%5Cfrac%7B1%7D%7B2%7Dx-338%29)
Finally, she spent $56 for gas. So, we will subtract 56:
![x-\frac{1}{2}x-338-\frac{1}{2}(x-\frac{1}{2}x-338)-56](https://tex.z-dn.net/?f=x-%5Cfrac%7B1%7D%7B2%7Dx-338-%5Cfrac%7B1%7D%7B2%7D%28x-%5Cfrac%7B1%7D%7B2%7Dx-338%29-56)
And we know that after all of the expenses, she will have $102 left. Therefore:
![x-\frac{1}{2}x-338-\frac{1}{2}(x-\frac{1}{2}x-338)-56=102](https://tex.z-dn.net/?f=x-%5Cfrac%7B1%7D%7B2%7Dx-338-%5Cfrac%7B1%7D%7B2%7D%28x-%5Cfrac%7B1%7D%7B2%7Dx-338%29-56%3D102)
We want to know how much Marlina spent on rent. So, let's find her salary x first.
First, let's distribute the 1/2:
![x-\frac{1}{2}x-338-\frac{1}{2}x+\frac{1}{4}x+169-56=102](https://tex.z-dn.net/?f=x-%5Cfrac%7B1%7D%7B2%7Dx-338-%5Cfrac%7B1%7D%7B2%7Dx%2B%5Cfrac%7B1%7D%7B4%7Dx%2B169-56%3D102)
Combine like terms:
![(x-\frac{1}{2}x-\frac{1}{2}x+\frac{1}{4}x)+(-338+169-56)=102](https://tex.z-dn.net/?f=%28x-%5Cfrac%7B1%7D%7B2%7Dx-%5Cfrac%7B1%7D%7B2%7Dx%2B%5Cfrac%7B1%7D%7B4%7Dx%29%2B%28-338%2B169-56%29%3D102)
Evaluate:
![\frac{1}{4}x-225=102](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7Dx-225%3D102)
Add 225 to both sides:
![\frac{1}{4}x=327](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7Dx%3D327)
Multiply both sides by 4:
![x=\$ 1308](https://tex.z-dn.net/?f=x%3D%5C%24%201308)
Therefore, Marlina received a total of $1308 for her salary.
We know that she spent half of her salary on rent. Therefore, the amount she spent on rent is:
![r=\frac{1}{2}(1308)=\$ 654](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B1%7D%7B2%7D%281308%29%3D%5C%24%20654)
And we're done!