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QuestionDonna wants a handbag priced at \$459. Calculate costs from two sellers and determine the better deal.
(a) Distributor marks up 50%. What’s the price?
(b) Boutique marks up 20% then 30%. What’s the price?
(c) Which is cheaper: distributor, boutique, or the same?

Studdy Solution

STEP 1

Assumptions1. The wholesale price of the handbag is $459. The distributor marks up the wholesale price by50% when selling directly to customers3. The boutique gets the handbag from a distributor who marks up the wholesale price by20%
4. The boutique then marks up the price by an additional30%
5. We are ignoring tax in this calculation

STEP 2

First, we need to find the price of the handbag when Donna buys it directly from the distributor. We can do this by adding the markup to the wholesale price.
Pricedistributor=Wholesale price+(Wholesale pricetimesMarkupdistributor)Price_{distributor} = Wholesale\, price + (Wholesale\, price \\times Markup_{distributor})

STEP 3

Now, plug in the given values for the wholesale price and distributor's markup to calculate the price.
Pricedistributor=$459+($459times50%)Price_{distributor} = \$459 + (\$459 \\times50\%)

STEP 4

Convert the percentage to a decimal value.
50%=0.50\% =0.Pricedistributor=$459+($459times0.)Price_{distributor} = \$459 + (\$459 \\times0.)

STEP 5

Calculate the price of the handbag from the distributor.
Pricedistributor=$459+($459times0.5)=$688.5Price_{distributor} = \$459 + (\$459 \\times0.5) = \$688.5

STEP 6

Next, we need to find the price of the handbag when Donna buys it from the boutique. We can do this by first calculating the price the boutique pays to the distributor, and then adding the boutique's markup.
Priceboutique=(Wholesale price+(Wholesale pricetimesMarkupdistributor))times(1+Markupboutique)Price_{boutique} = (Wholesale\, price + (Wholesale\, price \\times Markup_{distributor})) \\times (1 + Markup_{boutique})

STEP 7

Now, plug in the given values for the wholesale price, distributor's markup, and boutique's markup to calculate the price.
Priceboutique=($459+($459times20%))times(1+30%)Price_{boutique} = (\$459 + (\$459 \\times20\%)) \\times (1 +30\%)

STEP 8

Convert the percentages to decimal values.
20%=0.220\% =0.230%=0.330\% =0.3Priceboutique=($459+($459times0.2))times(1+0.3)Price_{boutique} = (\$459 + (\$459 \\times0.2)) \\times (1 +0.3)

STEP 9

Calculate the price of the handbag from the boutique.
Priceboutique=($459+($459times.2))times(+.3)=$689.85Price_{boutique} = (\$459 + (\$459 \\times.2)) \\times ( +.3) = \$689.85

STEP 10

Now that we have the prices from both the distributor and the boutique, we can compare them to find out where Donna would pay less.
If Pricedistributor<PriceboutiquePrice_{distributor} < Price_{boutique}, then Donna would pay less for the handbag if she gets it directly from the distributor.
If Pricedistributor>PriceboutiquePrice_{distributor} > Price_{boutique}, then Donna would pay less for the handbag if she gets it at the boutique.
If Pricedistributor=PriceboutiquePrice_{distributor} = Price_{boutique}, then Donna would pay the same amount if she gets the handbag from the distributor or at the boutique.

STEP 11

Compare the prices.
Since 688.5<689.85688.5 <689.85, Donna would pay less for the handbag if she gets it directly from the distributor.

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