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In a sale Tommy bought a kettle and a toaster. He paid a total of $105. The amount paid for the kettle is 2/5 the cost of the toaster. The total price before the discount should have been $133. The toaster was reduced by 20%. How much was the kettle reduced by?

 Nov 30, 2021
 #1
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Note:If we reduce a by b%, then final amount will

be = a - ab/100 

= a(100-b)/100.

Let the cost of the toaster is $x. 

Since the amount paid for the kettle is 2/5 the

cost of the toaster, then the cost of kettle will

be $ 2x/5.


 

 

 

 

According to the given conditions, 

x + 2x/5 = 105

Or, 7x/5 = 105

Or, x = 105*5/7 = 75

So, the cost of the toaster is = $75 and the cost of the kettle is = $(105-75) =$30.

Since the toaster was reduced by 20%, then before reduction its price was

 = $ 100*75/(100-20) = $ 93.75

Thus before reduction the price of kettle was = $(133-93.75) = $ 39.25

So, the percentage of reduction of the price of kettle is

 = ((39.25 - 30)*100)/30 = 23.5669%

Therefore required answer is 23.5669%.

 Nov 30, 2021
 #2
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Let the amount Paid for toaster = x

the amount Paid for Kettle = 2x/5

x + 2x/5 = 105

or (5x - 2x)/5 = 105

7x = 525

x = 75

Cost of Toaster = $75

Cost of Kettle = 2/5 * 75 = $30

Discount on Toaster = 20%
actual discount on toaster 

= 20/100 * 75 = $15

Total discount = 133 - 105 = $28

discount on Kettle = 28 - 15 = $13

Kettle was reduced by $13

 Apr 17, 2022
 #3
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Let the price of the toaster==T
The price of the kettle ==2/5T


T + 2/5T ==105, solve for T
T ==$75 - price of the toaster after 20%discount.
75 x 2/5==$30 -price of the kettle before 20% discount.


T x 0.80 ==$75, solve for T
T ==75 / 0.8 ==$93.75 - price of the toaster before 20% discount
133 - 93.75 ==$39.25 - price of the kettle before 20% discount.


1 - [30 / 39.25] ==23.567% - discount percentage on the kettle. 

 Apr 17, 2022
 #4
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Let toaster be Paid = x

Kettle Paid = 2/5x = 2x

Total 7x = 105

           x = 15

Kettle Price = 30

and Toaster Price = 75

Before discount Kettle Price 80% x = 30

                                => x = 30/80 * 100

                                     x = $37.5

Price of toaster before reduced = $95.5

 

reduced Price = 20.5/95.5 * 100

Kettle reduced = 21.4%

 Apr 18, 2022
 #5
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Total price before the discount -> $193

He paid -> $105

Suppose the price of toaster -> $x

the toaster was reduced 20%
                 = x * 80/100 = 1/5 = $4x/5

then, price paid of kettle = 4x/5 * 2/5

                                       = $8x/25

according to the clue

               4x/5 + 8x/25 = 105

             (20x + 8x)/25 = 105

                       x = 93.75 [Total price of kettle]

 reduced price of kettle = 4x/5 = 4 * 93.75/5

                                                  = $75

                       Difference = 93.75 - 75

                                        = $18.75

so, the kettle was reduced by $18.75

 Apr 18, 2022

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