Question

Marlina received her salary on Friday. She spent one-half of her salary on rent and then spent $338 on her electric and water bill. Next, she spent one-half of what was left on her phone bill. After spending $56.00 on gas for her car, Marlina had $102.00 left. How much did Marlin spend on rent?

Answer 1

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:

$x-\frac{1}{2}x-338$

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:

$x-\frac{1}{2}x-338-\frac{1}{2}(x-\frac{1}{2}x-338)$

Finally, she spent $56 for gas. So, we will subtract 56:

$x-\frac{1}{2}x-338-\frac{1}{2}(x-\frac{1}{2}x-338)-56$

And we know that after all of the expenses, she will have $102 left. Therefore:

$x-\frac{1}{2}x-338-\frac{1}{2}(x-\frac{1}{2}x-338)-56=102$

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:

$x-\frac{1}{2}x-338-\frac{1}{2}x+\frac{1}{4}x+169-56=102$

Combine like terms:

$(x-\frac{1}{2}x-\frac{1}{2}x+\frac{1}{4}x)+(-338+169-56)=102$

Evaluate:

$\frac{1}{4}x-225=102$

Add 225 to both sides:

$\frac{1}{4}x=327$

Multiply both sides by 4:

$x=\ 1308$

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:

$r=\frac{1}{2}(1308)=\ 654$

And we're done!