The net price after applying 40%, 12.5% and 7% to $628 can be obtained by multiplying $628 by the differences between 1 and the percent of discount.

`(628)(1-0.4)(1-0.125)(1-0.07)`

`=(628)(0.6)(0.875)(0.93)`

`=(376.80)(0.875)(0.93)`

`=(329.70)(0.93)`

`=306.621`

**The net price for the first line is $306.62.**

The total discount is `628-306.62=321.38`

The single equivalent rate...

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The net price after applying 40%, 12.5% and 7% to $628 can be obtained by multiplying $628 by the differences between 1 and the percent of discount.

`(628)(1-0.4)(1-0.125)(1-0.07)`

`=(628)(0.6)(0.875)(0.93)`

`=(376.80)(0.875)(0.93)`

`=(329.70)(0.93)`

`=306.621`

**The net price for the first line is $306.62.**

The total discount is `628-306.62=321.38`

The single equivalent rate of discount can be determined by dividing the total discounted amount by the total amount

`321.38/628=0.51`

**Thus the single equivalent rate of discount is 51%**

To verify, compute the difference between 1 and the factors used to calculate the net price:

`1-(0.6)(0.875)(0.93)=0.51`

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To determine the list price for the second line, divide $783.75 by the differences between 1 and the percent of discount.

`783.75/((1-0.35)(1-0.33)(1-0.12)`

`=783.75/((0.65)(2/3)(0.88))=2055.29`

` `**Therefore the list price for the second line is $2055.29**

The single equivalent rate of discount is:

`1-(0.65)(2/3)(0.88)=0.6187` or 61.87%

**The single equivalent rate of discount for the second line is 61.87%.**