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 mar…

Question

asked Jun 25, 2023 201k views

1 Answer

Graphite · Answer 1 · 2023-07-01T09:25:40+0000

Answer:

$\$ 400$ .

Explanation:

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

Rearrange the discount equation to solve for
in terms of
and
.

$S = R - r\, R$ .

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

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
and
to find the value of
:

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

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