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QuestionCompare refrigerator prices:
(a) Superstore markup of 40%40\% on \$699. How much does Sam pay?
(b) Department store with 20%20\% discount. What’s the price?
(c) Which is true? Superstore more expensive, department store more, or same price?

Studdy Solution

STEP 1

Assumptions1. The wholesale price of the refrigerator is $699. The superstore marks up the price by40%
3. The department store marks up the price by30%
4. The department store offers a20% discount on the marked-up price5. The markups and discount are calculated as a one-time adjustment, not compounding6. We are ignoring tax

STEP 2

First, we need to find the price of the refrigerator at the superstore. We can do this by adding the markup to the wholesale price.
Superstore price=Wholesale price+(Wholesale pricetimesSuperstore markup)Superstore\, price = Wholesale\, price + (Wholesale\, price \\times Superstore\, markup)

STEP 3

Now, plug in the given values for the wholesale price and superstore markup to calculate the superstore price.
Superstore price=$699+($699times40%)Superstore\, price = \$699 + (\$699 \\times40\%)

STEP 4

Convert the percentage to a decimal value.
40%=0.440\% =0.4Superstore price=$699+($699times0.4)Superstore\, price = \$699 + (\$699 \\times0.4)

STEP 5

Calculate the superstore price.
Superstore price=$699+($699times0.4)=$979.Superstore\, price = \$699 + (\$699 \\times0.4) = \$979.

STEP 6

Next, we need to find the price of the refrigerator at the department store before the discount. We can do this by adding the markup to the wholesale price.
Department store price=Wholesale price+(Wholesale pricetimesDepartment store markup)Department\, store\, price = Wholesale\, price + (Wholesale\, price \\times Department\, store\, markup)

STEP 7

Now, plug in the given values for the wholesale price and department store markup to calculate the department store price before discount.
Department store price=$699+($699times30%)Department\, store\, price = \$699 + (\$699 \\times30\%)

STEP 8

Convert the percentage to a decimal value.
30%=0.330\% =0.3Department store price=$699+($699times0.3)Department\, store\, price = \$699 + (\$699 \\times0.3)

STEP 9

Calculate the department store price before discount.
Department store price=$699+($699times.3)=$908.7Department\, store\, price = \$699 + (\$699 \\times.3) = \$908.7

STEP 10

Now, we need to find the price of the refrigerator at the department store after the discount. We can do this by subtracting the discount from the department store price before discount.
Department store price after discount=Department store price−(Department store pricetimesDiscount)Department\, store\, price\, after\, discount = Department\, store\, price - (Department\, store\, price \\times Discount)

STEP 11

Now, plug in the given values for the department store price before discount and discount to calculate the department store price after discount.
Department store price after discount=$908.7−($908.7times20%)Department\, store\, price\, after\, discount = \$908.7 - (\$908.7 \\times20\%)

STEP 12

Convert the percentage to a decimal value.
20%=0.220\% =0.2Department store price after discount=$908.7−($908.7times0.2)Department\, store\, price\, after\, discount = \$908.7 - (\$908.7 \\times0.2)

STEP 13

Calculate the department store price after discount.
Department store price after discount=$908.7−($908.7times0.2)=$726.96Department\, store\, price\, after\, discount = \$908.7 - (\$908.7 \\times0.2) = \$726.96

STEP 14

Now, we compare the prices at the two stores.
If the superstore price is greater than the department store price after discount, then Sam would pay more at the superstore. If the department store price after discount is greater than the superstore price, then Sam would pay more at the department store. If the two prices are equal, then Sam would pay the same at both stores.

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