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# After a series of discounts 6 23, a GPS had a net cost of 243.55. What is the list price of the GPS?

After a series of discounts 6 23, a GPS had a net cost of 243.55. What is the list price of the GPS?

If this is a series of discounts, one applied then the other, they compound each other and it's not correct to simply add them. Assuming 6 is 6% and is applied first, and 23 is 23% and applied second, we can solve this problem this way.

243.55/(1-.23) = 316.30
316.30/(1-.06) = 336.49

\$336.49 is the list price.

Check 336.49*(1-.06)=316.30
316.30*(1-.23)=243.55

Tammy, I responded to your question in a comment, but it didn't show up. Maybe the comment will show up later. But I will repeat my explanation here just in case.

If the discount is 6% and the price before discount is 336.49, then the price after discount is 1-.06.

The discount amount is 336.49*.06=20.19
The price after discount is 336.49-20.19=316.30 which is the same as 336.49*(1-.06).

If you want to undo the discount you do divide instead of multiply.

Truthfully, because multiplication (division is just multiplying by the reciprocal) is commutative, the order of the discounts doesn't matter. The compounding aspect of the discounts makes a difference though.
I do not understand how you got 316.30 or 336.49. Where does the 1 come from?

Thanks!
If the discount is a certain percentage, say 10%, then the amount after discount is 1-.10.

Example: Price is \$50. Discount is \$50*.10=\$5. Price after discount is \$50-\$5=\$45=\$50*.9

If you want to "undo" the discount, you divide by 1-disount.

Example: \$45/.9 = \$50.

Hope this clears it up.
Your 6 and 23 are unclear, are the numbers 6 and 23 percentages?  Or is 6 23 = 6.23 (total amount of discount)?

If the 6 and 23 are percentages, (NET implies final cost including tax deduction but since it does not specify, assume there is no tax)

243.55 is the net cost
let L stand for List price
29% = 0.29L (29% of list price, 23 + 6 = 29)

L - 0.29L = 243.55
1L - 0.29L = 243.55
0.71L = 243.55
L = 343.028, round to nearest penny = 343.03

total amount of the discount = 343.03 - 243.55 = 99.48

To check :  343.03 X 29% (0.29) = 99.48