A retail clothing store applies successive markdowns to a coat during a seasonal clearance… — ACT

A retail clothing store applies successive markdowns to a coat during a seasonal clearance sale. In the first week, the original price of the coat is discounted by $30\%$ . In the second week, the price is reduced by an additional $\frac{1}{5}$ of the first-week sale price. Finally, a customer uses a promotional code at checkout to receive an extra $15\%$ off the second-week sale price. If the customer pays a final price of $\$119.00$ before tax, what was the original price of the coat, in dollars?

Cevap: 250 dollars

Cevap

The original price of the coat was

250

dollars.

To find the original price of the coat, express each successive discount as a multiplier representing the portion of the remaining price. The first discount of

30\%

leaves

70\%

(

0.70

). The second discount of

\frac{1}{5}

(

20\%

) leaves

80\%

(

0.80

) of the first sale price. The final discount of

15\%

leaves

85\%

(

0.85

) of the second sale price. Combining these yields an overall price multiplier of

0.70 \times 0.80 \times 0.85 = 0.476

. Dividing the final purchase price of

\$119.00

0.476

gives the original price of

\$250.00

Adım Adım Çözüm

Calculate the price multiplier for the first week discount.

Multiplier 1 =

0.70

30\%

discount leaves

100\% - 30\% = 70\%

of the original price.

Convert the second week fraction discount to a decimal multiplier.

Multiplier 2 =

0.80

A discount of

\frac{1}{5}

is equal to

20\%

, leaving

1 - 0.20 = 0.80

of the week-1 price.

Calculate the price multiplier for the promotional code.

Multiplier 3 =

0.85

15\%

discount leaves

100\% - 15\% = 85\%

(

0.85

) of the week-2 price.

Find the combined price multiplier by taking the product of all three individual multipliers.

Combined Multiplier =

0.476

Successive discounts compound multiplicatively:

0.70 \times 0.80 \times 0.85 = 0.476

Solve for the original price

P

using the equation

0.476 P = 119

P = 250

Dividing the final price

\$119.00

0.476

yields

250

Anahtar Kavram

Compounding successive percentage and fraction discounts and solving for the original value.

Tahmini Süre:2m 0s

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