Answer to Question #154428 in Algebra for kris

Question

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?

Answer 1

a) Let the net price be represented by $N,$ the original list price by $L,$ the first rate of discount by $d_1,$ the second rate of discount by $d_2,$ the third rate of discount by $d_3$

$$N=L(1-d_1)(1-d_2)(1-d_3)$$

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

$$=\$443.79$$

The net price is $\$443.79.$

b)

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

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

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

c)

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

$$=1-(1-d_1)(1-d_2)(1-d_3)$$

$$=1-(1-0.36)(1-0.10)(1-0.02)$$

$$=0.43552$$

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