At a certain automobile dealership that sells only Tajimas and Franks

Question

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

This is a PS Butler Question

Check the links to other Butler Projects:

A. 20
B. 27
C. 48
D. 60
E. 87

This is a  PS Butler Question

Check the links to other Butler Projects:

Data Sufficiency Butler  
  Critical Reasoning Butler  
  Reading Comprehension Butler  
  Data Insights Butler

GMATinsight · Answer

Tajima
Hybrid=x
Non Hybrid=y

y = 3x-35
x+y = 205

i.e. x = 60 and y = 145

Franks
Hybrid=a
Non Hybrid=b

x:b = 5:4

i.e. b = 48

x+y+a+b = 280
i.e. a+b = 280-205 = 75

i.e. a = 75-48 = 27

Answer: Option B

ManifestDreamMBA · Answer

Let
NT = Non Hybrid Tajimas
NF = Non Hybrid Franks
HT = Hybrid Tajimas
HF = Hybrid Franks

NT = 3HT -35
NT + HT = 205
3HT -35+HT = 205
HT = 60
NT = 145

HT:NF = 5:4
60/NF = 5/4
NF = 48

Total = 280
280 = NT + HT + NF + HF
280 = 205 + 48 + HF
HF = 27

Gmat750aspirant · Answer

Step 1: Define variables 
Let T_h be the number of hybrid Tajimas. 
Let T_n be the number of nonhybrid Tajimas. 
Let F_h be the number of hybrid Franks. 
Let F_n be the number of nonhybrid Franks.

Step 2: Set up equations based on the problem statement

1. "The number of nonhybrid Tajimas is 35 less than 3 times the number of hybrid Tajimas": 
 T_n = 3T_h - 35

2. "205 total Tajimas are currently owned by the dealership": 
 T_h + T_n = 205

3. Substitute T_n from equation 1 into equation 2: 
 T_h + (3T_h - 35) = 205 
 4T_h - 35 = 205 
 4T_h = 240 
 T_h = 60

4. Find T_n using T_n = 3T_h - 35: 
 T_n = 3(60) - 35 = 180 - 35 = 145

Step 3: Set up equations for Franks

5. "The ratio of hybrid Tajimas to nonhybrid Franks is 5:4": 
 T_h / F_n = 5/4

6. Substitute T_h = 60: 
 60 / F_n = 5 / 4 
 Cross multiply: 
 5F_n = 240 
 F_n = 48

7. "280 total automobiles owned by the dealership": 
 T_h + T_n + F_h + F_n = 280 
 60 + 145 + F_h + 48 = 280 
 253 + F_h = 280 
 F_h = 27

Conclusion 
Answer: B (27)

Ayeka · Answer

Given: NHT=3HT-35
 HT+NHT=205= T 
 HT:NHF=5:4
 F+T=280 
To find: HF=?

HT+NHT=205 ; NHT=205-HT
NHT=3HT-35 ; 205-HT=3HT-35 ; HT= 60
HT:NHF=5:4 ; 60:NHF=5:4 ; NHF= 48
F+T=280 ; F=280-205 ; F=75 
NHF+HF=75=F ; 48+HF=75 ; HF=27

Answer: B

MagnusSamIBA · Answer

Let hybrid Tajimas = x
Then nonhybrid Tajimas = 3x - 35
So total Tajimas = x + (3x - 35) = 4x - 35
Set that equal to 205 → 4x - 35 = 205 → x = 60

Now from the ratio hybrid Tajimas : nonhybrid Franks = 5:4
So 60 : y = 5 : 4 → cross-mult y = 48

Now total cars = 280, Tajimas = 205 → Franks = 75
So hybrid Franks = 75 - 48 = 27

Ans: B

At a certain automobile dealership that sells only Tajimas and Franks

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

At a certain automobile dealership that sells only Tajimas and Franks

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards