Question

janice earns a 4 percent commission for the medical equipment that she sells. if she earned $1,823.34 in commission on the digital x - ray machine that she sold, what was the cost of the machine? $4,559.85 $7,295.76 $45,598.50 $72,957.60

Explanation:

Step1: Define the formula for commission

Commission ($C$) is calculated as a percentage ($r$) of the cost of the machine ($x$), so the formula is $C = r\times x$. Here, the commission rate $r = 4\%=0.04$ and the commission earned $C = 1823.34$.

Step2: Solve for the cost of the machine ($x$)

We need to find $x$, so we rearrange the formula to $x=\frac{C}{r}$. Substituting the values, we get $x=\frac{1823.34}{0.04}$.

Step3: Perform the division

Calculating $\frac{1823.34}{0.04}= 45583.5$? Wait, wait, maybe I misread the commission amount. Wait, looking at the image, maybe the commission is $1,823.34$? Wait, no, maybe the options: Wait, the options are $4,559.85$? Wait, no, let's check again. Wait, maybe the commission is $182.334$? Wait, no, the user's image: "she earned $1,823.34$ in commission"? Wait, no, maybe the numbers are: Wait, the options are $4,559.85$ (wait, no, $4,559.85$ times 4% is $182.394$, no. Wait, $45,598.50$ times 4% is $1,823.94$, which is close to $1,823.34$. Maybe a typo, but let's proceed. Wait, the correct calculation: if $C = 1823.34$ and $r = 0.04$, then $x=\frac{1823.34}{0.04}=45583.5$, but that's not an option. Wait, maybe the commission is $182.334$? Then $x=\frac{182.334}{0.04}=4558.35$, no. Wait, the options: $4,559.85$, $7,295.76$, $45,598.50$, $72,957.60$. Wait, $45,598.50$ times 4% is $45598.5\times0.04 = 1823.94$, which is very close to $1823.34$ (maybe a rounding difference). So probably the commission is $1823.94$ (maybe a typo in the problem), so $x = \frac{1823.94}{0.04}=45598.5$. So the cost of the machine is $45,598.50$.

Answer:

$\$45,598.50$ (the option with this value)