Math

QuestionEen handelaar kocht handtassen voor R172,00 en wil een korting van 14%14\% geven en toch 24%24\% winst maken. Wat moet de verkoopprijs zijn? a. R243,14. b. R248,00. c. R258,00. d. R183,42.

Studdy Solution

STEP 1

Assumptions1. The cost price of each handbag is R172,00. The merchant wants to make a24% profit on the cost price3. The merchant wants to offer a14% discount on the selling price4. The discount is calculated on the marked price, not the cost price5. The profit is calculated on the cost price, not the selling price

STEP 2

First, we need to find the selling price that would give the merchant a24% profit. We can do this by multiplying the cost price by1 plus the profit rate.
ellingprice=Costpricetimes(1+Profitrate)elling\, price = Cost\, price \\times (1 + Profit\, rate)

STEP 3

Now, plug in the given values for the cost price and profit rate to calculate the selling price.
ellingprice=R172,00times(1+24%)elling\, price = R172,00 \\times (1 +24\%)

STEP 4

Convert the percentage to a decimal value.
24%=0.2424\% =0.24ellingprice=R172,00times(1+0.24)elling\, price = R172,00 \\times (1 +0.24)

STEP 5

Calculate the selling price.
ellingprice=R172,00times1.24=R213,28elling\, price = R172,00 \\times1.24 = R213,28

STEP 6

Now that we have the selling price, we can find the marked price before discount. This is the price that, when discounted by14%, equals the selling price. We can find this by dividing the selling price by1 minus the discount rate.
Markedprice=Sellingprice/(1Discountrate)Marked\, price = Selling\, price / (1 - Discount\, rate)

STEP 7

Plug in the values for the selling price and the discount rate to calculate the marked price.
Markedprice=R213,28/(114%)Marked\, price = R213,28 / (1 -14\%)

STEP 8

Convert the percentage to a decimal value.
14%=0.1414\% =0.14Markedprice=R213,28/(10.14)Marked\, price = R213,28 / (1 -0.14)

STEP 9

Calculate the marked price.
Markedprice=R213,28/.86=R248,00Marked\, price = R213,28 /.86 = R248,00The price that the merchant should mark on the label is R248,00.

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