The List price is Not Given but the Net Price is $93.03 and the discount rate ( multiple discounts ) 25% 10 % and 8 1/3 % . I am having trouble with on calculating the discount amount and the List price.
Hello, diehardmath4!
This is a tricky one . . . We have to baby-talk oiur way through it.
The List Price is not given, but the Net Price is $93.03
and the discount rates (multiple discounts) were: $\displaystyle 25\%,\;10\%,\:8\tfrac{1}{3}\%$
Find the List Price and the Discount.
We were given discounts of: .$\displaystyle \frac{1}{4},\;\frac{1}{10},\,\text{ and }\frac{1}{12}$
This means we paid: .$\displaystyle \frac{3}{4},\:\frac{9}{10},\,\text{ and }\frac{11}{12}$ of the List Price.
. . (We paid $93.03)
So we have: .$\displaystyle \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: .$\displaystyle L \;=\;\frac{480}{297}(93.03) \;=\;150.351552$
Therefore, the List Price is: .$\displaystyle \$150.36$
. . . . . . .. The discount is: . .$\displaystyle \$57.33$
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Check
. . $\displaystyle \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} $