Trade Discount help

Hello, diehardmath4!

This is a tricky one . . . We have to baby-talk oiur way through it.

Quote:

The List Price is not given, but the Net Price is $93.03
and the discount rates (multiple discounts) were: $25\%,\;10\%,\:8\tfrac{1}{3}\%$

Find the List Price and the Discount.

We were given discounts of: . $\frac{1}{4},\;\frac{1}{10},\,\text{ and }\frac{1}{12}$

This means we paid: . $\frac{3}{4},\:\frac{9}{10},\,\text{ and }\frac{11}{12}$ of the List Price.
. . (We paid $93.03)

So we have: . $\frac{3}{4}\cdot\frac{9}{10}\cdot\frac{11}{12}\cdo t L \;=\;93.03 \quad\Rightarrow\quad \frac{297}{480}L \:=\:93.03$

Hence: . $L \;=\;\frac{480}{297}(93.03) \;=\;150.351552$

Therefore, the List Price is: . $\$150.36$
. . . . . . .. The discount is: . . $\$57.33$

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Check

. . $\begin{array}{ccc} \$150.36 & \text{List price} \\ -37.59 & \text{25\% off} \\ ---- \\ 112.77 & \text{net price} \\ -11.28 & \text{10\% off} \\ ---- \\ 101.49 & \text{net price} \\ -8.46 & 8\tfrac{1}{3}\%\text{ off} \\ ---- \\ \$93.03 & \text{Net Price} \end{array}$