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QuestionAnn wants to buy golf clubs for \$369. Calculate prices at a pro shop and a distributor, then compare them.
(a) Pro shop marks up by 10% then 40%. What is the final price? (b) Distributor marks up by 50%. What is the final price? (c) Which is cheaper? Pro shop, distributor, or the same?

Studdy Solution

STEP 1

Assumptions1. The wholesale price of the golf clubs is $369. . The distributor marks up the wholesale price by10%.
3. The pro shop marks up the distributor's price by an additional40%.
4. The distributor, when selling directly to customers, marks up the wholesale price by50%.
5. We are ignoring tax in this calculation.

STEP 2

First, let's find out how much the pro shop pays the distributor for the golf clubs. We can do this by adding the distributor's markup to the wholesale price.
istributor′s price=Wholesale price+(Wholesale price×Distributor′s markup)istributor's\, price = Wholesale\, price + (Wholesale\, price \times Distributor's\, markup)

STEP 3

Now, plug in the given values for the wholesale price and the distributor's markup to calculate the distributor's price.
istributor′s price=$369+($369×10%)istributor's\, price = \$369 + (\$369 \times10\%)

STEP 4

Convert the percentage to a decimal value.
10%=0.110\% =0.1istributor′s price=$369+($369×0.1)istributor's\, price = \$369 + (\$369 \times0.1)

STEP 5

Calculate the distributor's price.
istributor′s price=$369+($369×0.1)=$405.9istributor's\, price = \$369 + (\$369 \times0.1) = \$405.9

STEP 6

Now that we have the distributor's price, we can find out how much the pro shop sells the golf clubs for. We can do this by adding the pro shop's markup to the distributor's price.
Pro shop′s price=Distributor′s price+(istributor′s price×Pro shop′s markup)Pro\, shop's\, price = Distributor's\, price + (istributor's\, price \times Pro\, shop's\, markup)

STEP 7

Now, plug in the given values for the distributor's price and the pro shop's markup to calculate the pro shop's price.
Pro shop′s price=$405.9+($405.9×40%)Pro\, shop's\, price = \$405.9 + (\$405.9 \times40\%)

STEP 8

Convert the percentage to a decimal value.
40%=0.440\% =0.4Pro shop′s price=$405.+($405.×0.4)Pro\, shop's\, price = \$405. + (\$405. \times0.4)

STEP 9

Calculate the pro shop's price.
Pro shop′s price=$405.9+($405.9×.4)=$568.26Pro\, shop's\, price = \$405.9 + (\$405.9 \times.4) = \$568.26

STEP 10

Now, let's find out how much the distributor sells the golf clubs for when selling directly to customers. We can do this by adding the distributor's markup to the wholesale price.
istributor′s direct price=Wholesale price+(Wholesale price×Distributor′s direct markup)istributor's\, direct\, price = Wholesale\, price + (Wholesale\, price \times Distributor's\, direct\, markup)

STEP 11

Now, plug in the given values for the wholesale price and the distributor's direct markup to calculate the distributor's direct price.
istributor′s direct price=$369+($369×50%)istributor's\, direct\, price = \$369 + (\$369 \times50\%)

STEP 12

Convert the percentage to a decimal value.
50%=0.550\% =0.5istributor′s direct price=$369+($369×0.5)istributor's\, direct\, price = \$369 + (\$369 \times0.5)

STEP 13

Calculate the distributor's direct price.
istributor′s direct price=$369+($369×0.5)=$553.5istributor's\, direct\, price = \$369 + (\$369 \times0.5) = \$553.5

STEP 14

Now, we can compare the pro shop's price and the distributor's direct price to find out where Ann would pay less for the golf clubs.
If Pro shop′s price<Distributor′s direct pricePro\, shop's\, price < Distributor's\, direct\, price, then Ann would pay less at the pro shop.
If Pro shop′s price>Distributor′s direct pricePro\, shop's\, price > Distributor's\, direct\, price, then Ann would pay less if she gets them directly from the distributor.
If Pro shop′s price=Distributor′s direct pricePro\, shop's\, price = Distributor's\, direct\, price, then Ann would pay the same amount whether she gets the golf clubs from the distributor or at the pro shop.

STEP 15

Compare the pro shop's price and the distributor's direct price.
Since 568.26>553.5568.26 >553.5, Ann would pay less for the golf clubs if she gets them directly from the distributor.

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