Question

6 - 17. aura currently pays $800 each month to rent her apartment. due to inflation, however, her rent is increasing by $50 each year. meanwhile, her monthly take - home pay is $1500 and she predicts that her monthly pay will only increase by $15 each year. assuming that her rent and take - home pay will continue to grow linearly, will her rent ever equal her take - home pay? if so, when? and how much will rent be that year? hint: write two expressions, one for the amount aura pays to rent her apartment and another for her take - home pay. set the expressions equal to one another

Explanation:

Step1: Write the linear equations

Let \(x\) be the number of years.
The rent equation: \(y = 800+50x\) (initial rent is \(800\), increase of \(50\) per year).
The take - home pay equation: \(y = 1500 + 15x\) (initial pay is \(1500\), increase of \(15\) per year).

Step2: Set the two equations equal

$$
LATEXBLOCK0
$$

Step3: Find the rent amount

Substitute \(x = 20\) into the rent equation \(y=800 + 50x\).
\(y=800+50\times20=800 + 1000=1800\)

Answer:

Yes, her rent will equal her take - home pay. It will happen in \(20\) years. The rent that year will be \(\$1800\).