A compressor is listed for $804.20 less 36%, 10%, 2%.
Round your final answers properly to two decimal places.
a) What is the net price?
b) What is the total amount of discount allowed?
c) What is the single equivalent rate of discount in % form?
(a) To solve for the net , apply the formula for multiple discounts which is:
Net price `=` List price `(1 - d_1)(1-d_2)(1-d_3).... (1 - d_n)`
where d represents the rate of discount in decimal form.
Since there are only three rate of discount in the problem, then, formula stops at d3.
Net Price `=` List Price `(1 - d_1)(1-d_2)(1-d_3)`
Then, plug-in List Price = 804.20, d1=0.36, d2=0.10 and d3=0.02 .
Net Price `= 804.20(1-0.36)(1-0.10)(1-0.02)`
Net Price `= 804.20(0.64)(0.90)(0.98)`
Net Price `=804.20*0.56448`
Net Price `=453.95`
Hence, the net price of the compressor is $453.95 .
(b) To solve for the total amount of discount, subtract the net price from the listed price.
Total amount of Discount = Listed Price - Net Price
Total amount of Discount `= 804.20-453.95`
Total amount of Discount `= 350.25`
Thus, the total amount of discount is $350.25 .
(c) To solve for the single discount, use the formula for percent change.
Percent Change `=` `(Cha n g e i n P r ice)/(O r ig i n a l P r ice)*100`
Applying this to the problem above, it would be:
Percent Discount `= ` `(Total Amount of Discount)/(Listed Price)*100`
Percent Discount `=350.25/804.20*100`
Percent Discount `= 43.55`
Therefore, the equivalent single discount is 43.55% .