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At a certain automobile dealership that sells only Tajimas and Franks,

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Kauner
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At a certain automobile dealership that sells only Tajimas and Franks, [#permalink] New post   27 May 2016, 23:25
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76% (02:55) correct 24% (02:57) wrong based on 234 sessions
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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 ?
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B
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glatzekatze
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Re: At a certain automobile dealership that sells only Tajimas and Franks, [#permalink] New post   27 May 2016, 23:46
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Kauner wrote:
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 ?



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
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At a certain automobile dealership that sells only Tajimas and Franks, [#permalink] New post   27 May 2016, 23:51
Expert Reply
Kauner wrote:
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 ?


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
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Re: At a certain automobile dealership that sells only Tajimas and Franks, [#permalink] New post   14 Jun 2017, 03:11
Kauner wrote:
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 ?


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
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Re: At a certain automobile dealership that sells only Tajimas and Franks, [#permalink] New post   20 Jun 2017, 07:34
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Kauner wrote:
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


We can let n = the number of nonhybrid Tajimas and h = the number of hybrid Tajimas. Thus:

n = 3h - 35

Since a total of 205 Tajimas are currently owned by the dealership:

n + h = 205

3h - 35 + h = 205

4h = 240

h = 60

Since h = 60, n = 145.

We are also given that the ratio of hybrid Tajimas to nonhybrid Franks is 5:4 = 5x : 4x.

Since the number of hybrid Tajimas is 60, we can say that 5x = 60, or x = 12. Thus, there are 4(12) = 48 nonhybrid Franks.

Since there are 280 cars at the dealership, we can create the following equation in which f = the number of hybrid Franks.

280 = 60 + 145 + 48 + f

280 = 253 + f

27 = f

Answer: B
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Re: At a certain automobile dealership that sells only Tajimas and Franks, [#permalink]
20 Jun 2017, 07:34
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