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One-quarter of the cars that an automobile manufacturer pro
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06 Jun 2017, 06:37
06 Jun 2017, 06:37
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Question Stats:
55% (01:44) correct
44% (02:33) wrong based on 61 sessions
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One-quarter of the cars that an automobile manufacturer produces are sports cars, and the rest are sedans. If one-fifth of the cars that the manufacturer produces are red and one-third of the sports cars are red, then what fraction of the sedans is red?
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\(\frac{7}{45}\)
Re: One-quarter of the cars that an automobile manufacturer pro
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11 Oct 2017, 06:24
11 Oct 2017, 06:24
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Let's find a number for the total car that is suitable to our computations. Since we are going to divide this number by 4, 3 and 5, we can use 4*3*5 = 60.
Then, the number of sports car is 1/4*60 = 15, while the sedans are 3/4*60 = 45.
Red cars are 1/5*60 = 12, while red sport cars are 1/3*15 = 5.
Now in order to find the number of red sedans, we can take the remaining red cars as 12-5 = 7 and compute the fraction as 7/45.
Then, the number of sports car is 1/4*60 = 15, while the sedans are 3/4*60 = 45.
Red cars are 1/5*60 = 12, while red sport cars are 1/3*15 = 5.
Now in order to find the number of red sedans, we can take the remaining red cars as 12-5 = 7 and compute the fraction as 7/45.
Re: One-quarter of the cars that an automobile manufacturer pro
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26 Oct 2020, 05:37
26 Oct 2020, 05:37
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Let's start by dissecting the givens: -
We know that 1/4 of the total cars are Sport cars. ( Sport cars ---> 1/4 )
The rest are Sedan => 3/4 are Sedan cars. ( Sedan cars ---> 3/4 )
The Total Red cars is 1/5
Now of the Sport cars we know that 1/5 of them are Red => ( Sport cars --> 1/4 ---> 1/3 Red )
The question is to find the fraction of the Red Sedans => ( Sedan cars --> 3/4 ---> X . Red)
So total Red = Red Sport + Red Sedan
1/5 = (1/3)(1/4) + (X)(3/4)
will give us 5 + 45X = 12 => X = 7/45
We know that 1/4 of the total cars are Sport cars. ( Sport cars ---> 1/4 )
The rest are Sedan => 3/4 are Sedan cars. ( Sedan cars ---> 3/4 )
The Total Red cars is 1/5
Now of the Sport cars we know that 1/5 of them are Red => ( Sport cars --> 1/4 ---> 1/3 Red )
The question is to find the fraction of the Red Sedans => ( Sedan cars --> 3/4 ---> X . Red)
So total Red = Red Sport + Red Sedan
1/5 = (1/3)(1/4) + (X)(3/4)
will give us 5 + 45X = 12 => X = 7/45
