Answer to Question #154428 in Algebra for kris

Question #154428

A home gym is listed for $786.20 less 36%, 10%, and 2%. (a) What is the net price? (b) What is the total amount of discount allowed? (c) What is the exact single rate of discount that was allowed?


1
Expert's answer
2021-01-11T15:04:52-0500

a) Let the net price be represented by N,N, the original list price by L,L, the first rate of discount by d1,d_1, the second rate of discount by d2,d_2, the third rate of discount by d3d_3


N=L(1d1)(1d2)(1d3)N=L(1-d_1)(1-d_2)(1-d_3)

N=$786.20(10.36)(10.10)(10.02)N=\$786.20(1-0.36)(1-0.10)(1-0.02)


=$443.79=\$443.79

The net price is $443.79.\$443.79.


b)


Amount of discount=LNAmount\ of\ discount=L-N

=$786.20$443.79=$342.41=\$786.20-\$443.79=\$342.41

The total amount of discount allowed is $342.41.\$342.41.


c)


Single equivalent rate of discount\text{Single equivalent rate of discount}

=1(1d1)(1d2)(1d3)=1-(1-d_1)(1-d_2)(1-d_3)

=1(10.36)(10.10)(10.02)=1-(1-0.36)(1-0.10)(1-0.02)

=0.43552=0.43552

The exact single rate of discount that was allowed is 43.552%.43.552\%.



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