SOLUTION: Successive discounts of 30% are followed by 45% equal to what single discount? a) 60% b) 90% c) Cannot be determined d) 75% e) 539/2000%

Question 1171759: Successive discounts of 30% are followed by 45% equal to what single discount?
a) 60%
b) 90%
c) Cannot be determined
d) 75%
e) 539/2000%
Found 2 solutions by Solver92311, Theo:
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!

None of the answers, including "Cannot be determined" are correct. The answer can indeed be determined but the correct answer is not listed.

John

My calculator said it, I believe it, that settles it

From
I > Ø

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
30% discount makes the price 70% of what it would have been.
45% discount makes the price 55% of what it would have been.
70% * 55% makes the price 38.5% of what it would have been.
100% minus 38.5% gives a discount of 61.5%.
that's pretty close to 60% discount.
selection A is the closest to what the answer should be.

for example:
assume the price is 1000 dollars.
30% discount off of that is .3 * 1000 = 300 dollars.
the price becomes 1000 minus 300 = 700 dollars.
45% discount off of that is .45 * 700 = 315 dollars.
the price becomes 700 minus 315 = 385 dollars.
that's the final price after all the discounts.
the total discount is 300 + 315 = 615 dollars.
615 dollars divided by 1000 dollars = .615 = 61.5% total discount.
that's not exactly equal to any of the selections, but it is closest to 60%.

the final price was 385 dollars.
1000 dollars minus 60% of 1000 dollars = 1000 dollars minus 600 dollars = 300 dollars final price.
that's very close to 385 dollars that we calculated exactly.

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