What single rate of discount would be equivalent to a series of 25%/18%/10%?

A) 55.4%
B) 53.0%
C) 41.7%
D) 34.3%
E) 44.7%

To find the single equivalent discount rate for a series of discounts, we use the formula for successive discounts: $\text{Net Price Factor}=(1-d_1)(1-d_2)(1-d_3)$ , where $d_1,d_2,$ and $d_3$ are the decimal forms of the discounts. For 25%, 18%, and 10%, we have $d_1=0.25$ , $d_2=0.18$ , and $d_3=0.10$ . Thus, the Net Price Factor = $(1-0.25)(1-0.18)(1-0.10)=0.75\times 0.82\times 0.90$ . Calculating this gives a Net Price Factor of approximately 0.553. The equivalent single discount is $1-\text{Net Price Factor}=1-0.553=0.447$ or 44.7%.