Question

Choose the following:
The cost of two tables and three chairs is $\$600.$ If the table costs $\$50$ more than the chair. Find the cost of each chair and table.

• A. $\$100$ and $\$150$
• B. $\$150$ and $\$165$
• C. $\$125$ and $\$165$
• D. $\$165$ and $\$100$

Answer 1

The correct option is A $\$100$ and $\$150$

Let the cost of each chair is $x$ and that of each table is $y,$
Given,
The cost of two tables and three chairs is $\$600.$
$\therefore 3x+2y=600\dots \left(i\right)$
and the table costs $\$50$ more than the chair
$\therefore y=x+50\dots \left(ii\right)$

Step 1: Find the value of x
Substituting $y=x+50$ in $\left(i\right),$ we get
Equation $\left(i\right)$ $\to$ $3x+2y=600$
$3x+2(x+50)=600$
$\Rightarrow 3x+2x+100=600\Rightarrow 5x=600-100=500\Rightarrow x=\frac{500}{5}\Rightarrow x=100$

Step 2: Now, Find the value of y
Substitute $x=100$ in equation $\left(ii\right)$
Equation $\left(ii\right)$ $\to$ $y=x+40$
$y=100+50$
$\Rightarrow y=150$
$\therefore x=100,y=150$

Therefore, the cost of each chair is $\$100$ and that of each table is $\$150.$