# If the total discount on the cost of skis for the Ski Store was 35% after trade discounts of 18%, 9% 3% and an invoice discount for prompt payment, what was the invoice discount to two decimal places?

Let's x be the original cost. The total discount is 0.35x.

The first discount of 18% is equal to 0.18x and the cost after the discount is:

x-0.18x=0.82x

Apply the 9% discount to 0.82x to determine the second discount:

(0.09)(0.82x)=0.0738x and the cost after the second discount is:

0.82x-0.0738x=0.7462x

Apply the 3% to 0.7462x to determine the third discount:

(0.03)(0.7462x)=0.022386x and the cost after the third discount is

0.7462x-0.022386x=0.723814x

The total amount due after the invoice discount was:

x-0.35x=0.65x

Calculate the difference between the cost after the third discount and the total amount due:

0.723814x-0.65x=0.073812x

Determine what percentage from 0.723814x is 0.073812x:

`0.073812/0.723814=0.101976`  or 10.20%

Thus the invoice discount was 10.20%

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