Question

Solve. Use the discount equation

S = R − rR, where S is the sale price, R is the regular price, and r is the discount rate.

An exercise bike is on sale for $320, having been marked down 20% off the regular price. Find the regular price.

Answer 1

`\$ 400`.

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 (S)/(1 - r) = ((1 - r)\, R)/(1 - r)`.

`\begin{aligned}R &= (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 &= (S)/(1 - r) \\ &= (320)/(1 - 0.2) \\ &= (320)/(0.8) \\ &= 400\end{aligned}`.

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