Student Question

# 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.

So,

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% .