Question 1080864: 1) The difference between a discount of 35% and two successive discounts of 20% and 20% on a certain bill was $22.find the amount of the bill.
2) A shopkeeper marks the prices of his goods at 25% higher than the original price. After that he allows a discount of 12%.what profit or loss does he get?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 1) The difference between a discount of 35% and two successive discounts of 20% and 20% on a certain bill was 22.
find the amount of the bill.
let x equal the amount of the bill.
a discount of 35% on the bill makes the bill equal to x - .35 * x = (1 - .35) * x = .65 * x.
the first discount of 20% on the bill makes the bill equal to x - .20 * x = .80 * x.
the second discount of 20% on the bill makes the bill equal to .80 * x - .20 * .80 * x which is equal to .80 * x - .16 * x which is equal to .64 * x.
the difference between a 35% discount on the original amount and two successive discounts of 20% on the original amount is .65 * x - .64 * x which is equal to .01 * x.
that difference is equal to 22, so you get .01 * x = 22.
solve for x to get x = 22/.01 = 2200.
the original amount was 2200.
a 35% discount on the original amount was .35 * 2200 = 770.
the discounted price was therefore 2200 - 7700 = 1430.
1430 is equal to 1430/2200 * 100 = 65% of the original cost, as we had calculated earlier.
a 20% discount on the original amount was .20 * 2200 = 440.
the first discounted price was therefore 2200 - 440 = 1760.
an additional discount of 20% on this amount was .20 * 1760 = 352.
the second discounted price was therefore 1760 - 352 = 1408.
1408 is equal to 1408 / 2200 * 100 = 64% of the original cost, as we had calculated earlier.
the difference between the 35% discounted price and the 20% on top of 20% discounted price is 1430 - 1408 = 22.
this confirms the solution is correct.
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2) A shopkeeper marks the prices of his goods at 25% higher than the original price. After that he allows a discount of 12%.
what profit or loss does he get?
let x equal the original price.
he marks it up by 25% which makes the marked price equal to x + .25 * x which is equal to 1.25 * x.
he gives a discount of 12% on this marked up price.
the discounted price is equal to 1.25 * x - .12 * 1.25 * x
simplify this to get the discounted price is equal to 1.25 * x - .15 * x.
combine like terms to get the discounted price is equal to 1.10 * x.
the original price was x.
the final discounted price off the marked up price is equal to 1.10 * x.
the difference is 1.10 * x - x which is equal to .10 * x.
thismeans the profit is equal to .10 * x which is equal to 10% of x which is equal to 10% of the original price.
to see if this makes sense, let x be any value.
i let x = 1000.
the marked up price is 1000 + .25 * 1000 = 1250.
a 12% discount on the marked price makes the discounted marked up price equal to 1250 - .12 * 1250 = 1100.
the original price was 1000.
the discounted marked up price was 1100.
the profit was 1100 - 1000 = 100 which is equal to 10% of the original price.
this confirms the solution was correct.
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