Question

What is the net decimal equivalent of the series 30/25/15. round to the nearest thousandths?

Answer 1

We can determine, a 30/25/15 series trade discount would be calculated as follows:

let X = retail price.

X - 0.30 × X = Y    ⇒ first discounted price.

Y - 0.25 × Y = Z    ⇒ second discounted price.

Z - 0.15*Z = T        ⇒ total discounted price.

X - 0.30 × X = (1 - 0.30) × X = 0.70 × X = Y

Y - 0.25 × Y = (1 - 0.25) × Y = 0.75 × Y = Z

Z - 0.15 × Z  = (1 - 0.15) × Z  = 0.85 × Z = T

since Z = 0.85 × Y, then 0.85 × Z = 0.85 × 0.75 × Y

since Y = 0.70 × X, then 0.85 × Z = 0.85 × 0.75 × 0.70 × X

based on the above, then T = total discount


                                               = 0.85 × 0.75 × 0.70 × X


                                               = 0.44625X

30/25/15 series discount is equivalent to a total discount of 44.625%

Answer 2

The  net decimal equivalent of the series 30/25/15 is 44.625%

Calculation of the net decimal:

Here we assume let X be retail price.

So,

X - 0.30 × X = Y    ⇒ first discounted price.

Y - 0.25 × Y = Z    ⇒ second discounted price.

Z - 0.15*Z = T        ⇒ total discounted price.

Now

X - 0.30 × X = (1 - 0.30) × X = 0.70 × X = Y

Y - 0.25 × Y = (1 - 0.25) × Y = 0.75 × Y = Z

Z - 0.15 × Z  = (1 - 0.15) × Z  = 0.85 × Z = T

Also, Z = 0.85 × Y, then 0.85 × Z = 0.85 × 0.75 × Y

And, Y = 0.70 × X, then 0.85 × Z = 0.85 × 0.75 × 0.70 × X

So,

 = 0.85 × 0.75 × 0.70 × X

 = 0.44625X

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