Question Kareem is deciding between two washing machines priced at $\$ 650$ . The first is $40\%$ off, the second is $10\%$ off with an additional $30\%$ off. Find the sale price of each and explain why Kareem should buy the first.

Studdy Solution

STEP 1

Assumptions
1. The selling price of each washing machine is $650.
2. The first washing machine is marked down by 40%.
3. The second washing machine is marked down by 10%, with an additional 30% off the discounted price.
4. Round to the nearest dollar if necessary.

STEP 2

Calculate the discount amount for the first washing machine. To do this, multiply the selling price by the discount rate.
$Discount\, amount\, for\, first\, machine = Selling\, price \times Discount\, rate$

STEP 3

Now, plug in the given values for the selling price and discount rate for the first washing machine to calculate the discount amount.
$Discount\, amount\, for\, first\, machine = \$650 \times 40\%$

STEP 4

Convert the percentage to a decimal value for calculation.
$40\% = 0.4$
$Discount\, amount\, for\, first\, machine = \$650 \times 0.4$

STEP 5

Calculate the discount amount for the first washing machine.
$Discount\, amount\, for\, first\, machine = \$650 \times 0.4 = \$260$

STEP 6

Subtract the discount amount from the selling price to find the sale price of the first washing machine.
$Sale\, price\, of\, first\, machine = Selling\, price - Discount\, amount\, for\, first\, machine$

STEP 7

Plug in the values to calculate the sale price of the first washing machine.
$Sale\, price\, of\, first\, machine = \$650 - \$260$

STEP 8

Calculate the sale price of the first washing machine.
$Sale\, price\, of\, first\, machine = \$650 - \$260 = \$390$

STEP 9

Calculate the discount amount for the second washing machine after the initial 10% discount. Multiply the selling price by the initial discount rate.
$Initial\, discount\, amount\, for\, second\, machine = Selling\, price \times Initial\, discount\, rate$

STEP 10

Now, plug in the given values for the selling price and initial discount rate for the second washing machine to calculate the initial discount amount.
$Initial\, discount\, amount\, for\, second\, machine = \$650 \times 10\%$

STEP 11

Convert the percentage to a decimal value for calculation.
$10\% = 0.1$
$Initial\, discount\, amount\, for\, second\, machine = \$650 \times 0.1$

STEP 12

Calculate the initial discount amount for the second washing machine.
$Initial\, discount\, amount\, for\, second\, machine = \$650 \times 0.1 = \$65$

STEP 13

Subtract the initial discount amount from the selling price to find the intermediate price before the additional discount.
$Intermediate\, price\, for\, second\, machine = Selling\, price - Initial\, discount\, amount\, for\, second\, machine$

STEP 14

Plug in the values to calculate the intermediate price for the second washing machine.
$Intermediate\, price\, for\, second\, machine = \$650 - \$65$

STEP 15

Calculate the intermediate price for the second washing machine.
$Intermediate\, price\, for\, second\, machine = \$650 - \$65 = \$585$

STEP 16

Calculate the additional discount amount for the second washing machine by multiplying the intermediate price by the additional discount rate.
$Additional\, discount\, amount\, for\, second\, machine = Intermediate\, price \times Additional\, discount\, rate$

STEP 17

Now, plug in the given values for the intermediate price and additional discount rate for the second washing machine to calculate the additional discount amount.
$Additional\, discount\, amount\, for\, second\, machine = \$585 \times 30\%$

STEP 18

Convert the percentage to a decimal value for calculation.
$30\% = 0.3$
$Additional\, discount\, amount\, for\, second\, machine = \$585 \times 0.3$

STEP 19

Calculate the additional discount amount for the second washing machine.
$Additional\, discount\, amount\, for\, second\, machine = \$585 \times 0.3 = \$175.5$

STEP 20

Subtract the additional discount amount from the intermediate price to find the sale price of the second washing machine.
$Sale\, price\, of\, second\, machine = Intermediate\, price - Additional\, discount\, amount\, for\, second\, machine$

STEP 21

Plug in the values to calculate the sale price of the second washing machine.
$Sale\, price\, of\, second\, machine = \$585 - \$175.5$

STEP 22

Calculate the sale price of the second washing machine.
$Sale\, price\, of\, second\, machine = \$585 - \$175.5 = \$409.5$

STEP 23

Round the sale price of the second washing machine to the nearest dollar.
$Sale\, price\, of\, second\, machine \approx \$410$

STEP 24

Now compare the sale prices of both washing machines to determine which one Kareem should buy.
$Sale\, price\, of\, first\, machine = \$390$ $Sale\, price\, of\, second\, machine \approx \$410$

STEP 25

Since the sale price of the first washing machine is lower than that of the second, Kareem should buy the first washing machine if the only difference is the selling price.
The sale price of the first washing machine is $390.

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