Answer
The units of one-bedroom condominiums sold is $=15$ units.
The units of two-bedroom condominiums sold is $=35$ units.
Work Step by Step
Step 1:- Assume unknown quantities as variables.
Let the units of one-bedroom condominiums sold be $=x$.
Let the units of two-bedroom condominiums sold be $=y$.
Step 2:- Write the system of equations.
The given values are
Total units sold $= \$50$
Total sales $=\$7050$
Selling price of each one-bedroom condominium is $\$120$ thousand
Selling price of each two-bedroom condominium is $\$150$ thousand
In the equation form
$\Rightarrow x+y=50$ ...... (1)
$\Rightarrow 120x+150y=7050$ ...... (2)
Step 3:- Solve the system of equations.
Multiply the equation (1) by $(-120)$.
$\Rightarrow (-120)x+(-120)y=(-120)50$
$\Rightarrow -120x-120y=-6000$ ...... (3)
Add equation (2) and (3).
$\Rightarrow 120x+150y-120x-120y=7050-6000$
Simplify.
$\Rightarrow 30y=1050$
Divide both sides by $30$.
$\Rightarrow \frac{30y}{30}=\frac{1050}{30}$
Simplify.
$\Rightarrow y=35$
Plug the value of $y$ into equation (1).
$\Rightarrow x+(35)=50$
Isolate $x$.
$\Rightarrow x=50-35$
Simplify.
$\Rightarrow x=15$.
Step 4:- Check the answers.
Substitute the values of $x$ and $y$ into equation (2).
$\Rightarrow 120(15)+150(35)=7050$
$\Rightarrow 1800+5250=2.88$
$\Rightarrow 7050=7050$. True.
