Question

Solve. Use the discount equation

Answer 1

Answer:

$\ 400$.

Step-by-step explanation:

In this question, $S$ (sales price) and $r$ (discount rate) are both given. The unknown is the regular price, $R$.

Rearrange the discount equation to solve for $R$ in terms of $S$ and $r$.

$S = R - r\, R$.

$S = (1 - r)\, R$.

Divide both sides by $(1 - r)$:

$\displaystyle \frac{S}{1 - r} = \frac{(1 - r)\, R}{1 - r}$.

$\begin{aligned}R &= \frac{S}{1 - r}\end{aligned}$.

It is given that $S = 320$. A mark-down of $20\%$ is equivalent to a discount rate of $r = 20 / 100 = 0.20$. Substitute in $S$ and $r$ to find the value of $R$:

$\begin{aligned}R &= \frac{S}{1 - r} \\ &= \frac{320}{1 - 0.2} \\ &= \frac{320}{0.8} \\ &= 400\end{aligned}$.

Thus, the regular price would be $\ 400$.