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At a certain automobile dealership

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by Vincen » Mon Sep 25, 2017 7:09 pm
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

The OA is B.

I got confused. Can any expert help me here. The ratio confuses me.
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by Jay@ManhattanReview » Mon Sep 25, 2017 10:45 pm
Vincen 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

The OA is B.

I got confused. Can any expert help me here. The ratio confuses me.
Say the number of hybrid Tajimas = x

Thus, the number of nonhybrid Tajimas = 3x - 35

We know that the total number of Tajimas = 205

Thus, x + (3x - 35) = 205

x = 60

Given that the ratio of hybrid Tajimas to nonhybrid Franks is 5 : 4, the number of nonhybrid Franks = (4/5)*(number of hybrid Tajimas) = (4/5)*(60) = 48

The number of nonhybrid Franks = 48

We know that the total number of automobiles = 280

Thus, the total number of Franks = 280 - 205 = 75

Again, the number of hybrid Franks + the number of nonhybrid Franks = 75

The number of hybrid Franks = 75 - The number of nonhybrid Franks = 75 - 48 = 27.

The correct answer: B

Hope this helps!

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by Matt@VeritasPrep » Tue Sep 26, 2017 4:55 pm
Start with the Tajimas. We've got 205 of them. Call the hybrids h and the nonhybrids n. That gives us

h + n = 205
n = 3h - 35

Solve that system: h = 60, n = 145

Since h = 60 and the ratio of h : nonhybrid Franks = 5 : 4, we know nonhybrid Franks = 48.

We've got 75 total Franks, meaning there are 27 left over, all of which must be hybrids.
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by Matt@VeritasPrep » Tue Sep 26, 2017 4:56 pm
Footnote: this question is designed to waste time and test your speed. There are a couple like this (at least) on every exam, so if the clock is against you and you're feeling overwhelmed, this is a good one on which to make a quick educated guess to get past.
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by Scott@TargetTestPrep » Fri Dec 15, 2017 10:09 am
Vincen 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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