Answer
The cost of one pad $=\$0.80$.
The cost of one pen $=\$0.20$.
Work Step by Step
Step 1:- Assume unknown quantities as variables.
Let the cost of one pad $=x$.
Let the cost of one pen $=y$.
Step 2:- Write system of equations.
The given values are
Cost of $2$ pads and $19$ pens equals $\$5.40$.
and cost of $7$ pads and $4$ pens equals $\$6.40$.
In the equation form.
$\Rightarrow 2x+19y=5.40$ ...... (1)
$\Rightarrow 7x+4y=6.40$ ...... (2)
Step 3:- Solve the system of equations.
Multiply the equation (1) by $7$ and equation (2) by $-2$.
$\Rightarrow 14x+133y= 37.80$ ...... (3)
$\Rightarrow -14x-8y=-12.80$ ...... (4)
Add equation (3) and (4).
$\Rightarrow 14x+133y-14x-8y=37.80-12.80$
Simplify.
$\Rightarrow 125y=25$
Divide both sides by $125$.
$\Rightarrow \frac{125y}{125}=\frac{25}{125}$
Simplify.
$\Rightarrow y=0.20$
Plug the value of $y$ into equation (1).
$\Rightarrow 2x+19(0.20)=5.40$
Simplify.
$\Rightarrow 2x+3.80=5.40$
Isolate $x$.
$\Rightarrow x=\frac{5.40-3.80}{2}$
Simplify.
$\Rightarrow x=0.80$.
Step 4:- Check the answers.
Substitute the values of $x$ and $y$ into equation (2).
$\Rightarrow 7(0.80)+4(0.20)=6.40$
$\Rightarrow 5.60+0.80=6.40$
$\Rightarrow 6.40=6.40$. True.
