A total of 40 brand X television sets and 80 brand Y television sets

Question

A total of 40 brand X television sets and 80 brand Y television sets were purchased for a motel chain. If the price of each brand Y set was twice the price of each brand X set, what percent of the total bill was the price of a brand Y set?

(A) 0.25%
(B) 0.5%
(C) 0.625%
(D) 0.833%
(E) 1.0%

(A) 0.25%
(B) 0.5%
(C) 0.625%
(D) 0.833%
(E) 1.0%

AkshdeepS · Accepted Answer

The question has asked for percentage, therefore I multiplied by 100.

160/200 x 100 = 80 %

Now, this 80% is for all set Y TVs, but the question asks for one set Y.

We have 80 set Y TVs.

So, for one set ( \frac{80}{80} )% = 1%

MathRevolution · Answer

X brand: 40 and Y brand: 80

Let the price of each X brand be $100. Therefore, the price of each Y brand will be $200.

Total price: (40 * 100) + (80 * 200) = 4,000 + 16,000 = 20,000

=>  \frac{(16,000 * 100)}{ 20,000}  = 80.

Price of 1 brand Y:  \frac{80 }{ 80}  = 1

Answer E

AkshdeepS · Answer

Brand X = 40 sets, Say price is $1.00 per set

Brand Y = 80 sets, price will be $2.00 per set as per question.

Total price for all X and Y TV sets = 40*1 + 80*2 = $ 200.00

Price of 80 sets of Brand Y = $ 160.00

Percent of the total bill was the price of  a brand Y set  is ;

\frac{(160*100)}{(200 * 80)}  = 1.00 %

Saransh123 · Answer

I have solved this problem like this
Let the cost of each TV of brand X be a, and cost of each TV of brand Y be b. 
Total Cost of 40 TV or X = 40a
Total Cost of 80 TV or Y= 80b
Given that price of each TV of brand Y is twice of brand A, therefore Y=2X, 80b=2*40a,b=a or 1%, Is it the correct method?

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TheBunk · Answer

Why do you multiply by 100 on the numerator and by 80 on the denominator ?

I can't understand why we don't just divide 160 (the price of the Y set) by 200 (total cost).

Thanks.

GinoRako · Answer

Let the price of brand X be $5,00, then the price of brand Y would be 2*($5,00)= $10,00

Total bill= 40 * ($5,00) + 80 * ($10,00)= $200 + $800 = $1000
 
Pay attention to the wording of the final sentence: What percent of the total bill, which is $1000 according the above calculation, was the price of a(the word  a  means 1 brand Y set) brand Y set, which is $10,00 according the above calculation.

Since the price of just one Brand Y is $10,00 and the total bill is $1000, then $10/$1000 = 0,01 or 1% or choice E

I hope it is clear.

HildaT · Answer

I have the same concern, why multiply by 100 and divide by total times 80? Is the total cost of Y over the total cost of X and Y insufficient to solve the problem?

Bunuel · Answer

The question asks what percent of the total bill is the price of  one  brand Y television. Assuming the price of each brand X television is $1 and each brand Y television is $2, the total bill would be (40 * $1 + 80 * $2) = $200. We are asked to find what percent of $200 is one brand Y television, which costs $2. The answer is 1%.

Hope this helps.

lavanya.18 · Answer

The total cost of the televisions:
Cost of 40 brand X televisions = 40*1=40
Cost of 80 brand Y televisions = 80*2=160
Total bill = 40+160=200

Percent of the total bill is the price of one brand Y television:

The price of one brand Y television is $2.
The percentage is:
2/200*100=1%

MihirBathia · Answer

I was searching for the option that said 80%, and luckily it was not there. Time and again I am reminded that the test continues to be an English test even beyond the English section.

A total of 40 brand X television sets and 80 brand Y television sets

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