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27 May 2016, 23:46
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B
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Difficulty:
35%
(medium)
Question Stats:
76% (02:53) correct
24%
(03:04)
wrong
based on 258
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Kauner
At a certain automobile dealership that sells only Tajimas and Franks, the number of nonhybrid Tajimas is 35 less than 3 times the number of hybrid Tajimas. 205 total Tajimas are currently owned by the dealership. If the ratio of hybrid Tajimas to nonhybrid Franks is 5:4 and there are 280 total automobiles owned by the dealership, how many hybrid Franks are there?
a 20
b 27
c 48
d 60
e 87
took me >120 seconds to solve this, is there an easier way ?
a 20
b 27
c 48
d 60
e 87
took me >120 seconds to solve this, is there an easier way ?
that's how I did it:
First, I only focus on Tajimas. Let x be hybrid Tajimas and y be nonhybrid Tajimas. We know that x + y = 205 and we know that y=3x-35, Therefore we can conclude that x= 60 and y= 145
Next, let a be the number of nonhybrid franks, we know the ratio, 60/a = 5/4, therefore a=48
Total number of franks is 75, so 75 - 48 = 27
Took me 47 sec.
These are a lot of steps, but they are easy, so they are doable in a couple of seconds, but probably, there is still an easier way
27 May 2016, 23:51
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Kauner
At a certain automobile dealership that sells only Tajimas and Franks, the number of nonhybrid Tajimas is 35 less than 3 times the number of hybrid Tajimas. 205 total Tajimas are currently owned by the dealership. If the ratio of hybrid Tajimas to nonhybrid Franks is 5:4 and there are 280 total automobiles owned by the dealership, how many hybrid Franks are there?
a 20
b 27
c 48
d 60
e 87
took me >120 seconds to solve this, is there an easier way ?
a 20
b 27
c 48
d 60
e 87
took me >120 seconds to solve this, is there an easier way ?
hi,
lets concentrate on T first as all details are available..
\(T_{nh} = 3T_{h} - 35........................and.. T_h + T_{nh} = 205....\)
so \(T_h + 3T_{h} - 35 = 205....................4T_h=240..................T_h=60\)..
now
\(F_{nh} = \frac{4T_{h}}{5} = \frac{240}{5} = 48.\)......
\(F_T = T - T_T = 280-205 = 75\)....
so \(F_h = F_T - F_nh = 75-48 = 27\)
Or
use a 2*2 matrix
\(..........NH.........H........Total\)...
\(T.......3x-35..........x.......205\)...
\(F........\frac{4x}{5}.........?....... 75\)..
\(total..........................280\)
B
14 Jun 2017, 03:11
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Kauner
At a certain automobile dealership that sells only Tajimas and Franks, the number of nonhybrid Tajimas is 35 less than 3 times the number of hybrid Tajimas. 205 total Tajimas are currently owned by the dealership. If the ratio of hybrid Tajimas to nonhybrid Franks is 5:4 and there are 280 total automobiles owned by the dealership, how many hybrid Franks are there?
a 20
b 27
c 48
d 60
e 87
took me >120 seconds to solve this, is there an easier way ?
a 20
b 27
c 48
d 60
e 87
took me >120 seconds to solve this, is there an easier way ?
Franks = 280 - 205 = 75
Let hybrid Tajimas = X , So nonhybrid Tajimas = 3X-35
Now ,
X + ( 3X -35 ) = 205
=> 4X = 240
=> X = 60
So , from 5 : 4
5X = 60
X = 12
Nonhybrid frank = 4*12 = 48
Hybrid frank = 75 - 48 = 27
Answer : B
