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16 Sep 2014, 01:10
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In the fleet of a certain car rental agency, the ratio of the number of sedans to the number of hatchbacks was 9:8. After adding 3 sedans and 1 hatchback to the fleet, this ratio increased to 6:5. How many more sedans than hatchbacks does the agency have after these additions?
A. 2
B. 3
C. 5
D. 7
E. 9
A. 2
B. 3
C. 5
D. 7
E. 9
16 Sep 2014, 01:10
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Bookmarks
Official Solution:
In the fleet of a certain car rental agency, the ratio of the number of sedans to the number of hatchbacks was 9:8. After adding 3 sedans and 1 hatchback to the fleet, this ratio increased to 6:5. How many more sedans than hatchbacks does the agency have after these additions?
A. 2
B. 3
C. 5
D. 7
E. 9
Let \(H\) and \(S\) represent the number of hatchbacks and sedans in the fleet before the addition of new cars, respectively. We can create a system of equations:
\(\frac{S}{H} = \frac{9}{8}\)
\(\frac{S + 3}{H + 1} = \frac{6}{5}\)
By solving this system of equations, we find that \(S = 27\) and \(H = 24\). After the additions, the agency has 30 sedans and 25 hatchbacks. Therefore, the agency has 5 more sedans than hatchbacks.
Answer: C
In the fleet of a certain car rental agency, the ratio of the number of sedans to the number of hatchbacks was 9:8. After adding 3 sedans and 1 hatchback to the fleet, this ratio increased to 6:5. How many more sedans than hatchbacks does the agency have after these additions?
A. 2
B. 3
C. 5
D. 7
E. 9
Let \(H\) and \(S\) represent the number of hatchbacks and sedans in the fleet before the addition of new cars, respectively. We can create a system of equations:
\(\frac{S}{H} = \frac{9}{8}\)
\(\frac{S + 3}{H + 1} = \frac{6}{5}\)
By solving this system of equations, we find that \(S = 27\) and \(H = 24\). After the additions, the agency has 30 sedans and 25 hatchbacks. Therefore, the agency has 5 more sedans than hatchbacks.
Answer: C
16 Sep 2016, 06:47
Kudos
Bookmarks
I always use this format when working with ratios: 9x/8x - the initial ratio. (9x+3)/(8x+1)=6/5 x=3
