A total of n trucks and cars are parked in a lot. If the num

Question

A total of n trucks and cars are parked in a lot. If the number of cars is 1/4 the number of trucks, and 2/3 of the trucks are pickups, how many pickups, in terms of n, are parked in the lot?

A. 1/6 n
B. 5/12 n
C. 1/2 n
D. 8/15 n
E. 11/12 n

I decided to use 100 for the total of trucks + cars. So n = 100.
Number of cars = 1/4 # of trucks, then there are 25 cars and 75 trucks
2/3 of the trucks are pickups, so 2/3 of 75 is 50.

Therefore, the number of pickups (50) in terms of n would be (1/2)n, which equals 100 * 1/2 = 50, the number of pickups. = C

However, this is not the correct answer- the correct answer is D, 8/15. Can someone explain???

KarishmaB · Accepted Answer

Try and use ratios where possible. They make your life very easy.

No of cars : No of trucks = 1:4 (Since for every 4 trucks, there is 1 car) 
So total cars and trucks (n) in ratio terms = 1+4 = 5
Now out of 4 trucks, 2/3 are pickup (p) i.e. 4*2/3 = 8/3 are pick up.
So p/n = (8/3)/5 or p = 8/15 n

Economist · Answer

n = t+c.
c=1/4 *t 
so the total number of vehicles in terms of t is n=5/4 *t
Now, 2/3 * t are pickups

Q asks: 2/3 * t = n * F ( F is the required fraction )
2/3 * t = 5/4 * F => F = 8/15.

Mongolia2HBS · Answer

D.
x+x/4=n => x=4n/5 => 2x/3=8n/15

shrouded1 · Answer

Let there be c cars and t trucks and p pickup trucks
n = t+c
t=4c
So n = 5c
(2/3)t = p
p = (2/3)t = (2/3)(4c) = (8/3)c = (8/3)(n/5) = (8/15)n

Answer is (d)

Capricorn369 · Answer

Lets consider the number of trucks = x
Hence, total number of cars is = x/4
 from the question we know, x+x/4 = n = > x = 4n/5
Number of trucks that are pickups = (2/3)4n/5 = 8n/15.
D is the answer.

Cheers!

prasannajeet · Answer

Lets say Total truck is 12. So car is 3.
Now pickups are =2/3rd of 12= 8
so total fraction is 8/15 ..ans

GSBae · Answer

C = Cars, T = Trucks, and P = Pickups.

C + T = n

C = \frac{1}{4} T 
 \frac{2}{3}T = P

We'd like to write everything in terms of Pickups, since that's what the question is asking us about. Thus,

T = \frac{3}{2}P ,
 C = \frac{1}{4}T = \frac{1}{4} * \frac{3}{2} P = \frac{3}{8}P

Therefore,

n = C + T = \frac{3}{8} P + \frac{3}{2} P = \frac{30}{16}P = \frac{15}{8}P.

Solving for P, we see that  P = \frac{8}{15} n.

Answer: D

NoHalfMeasures · Answer

This is all variables in answer choices question. So lets pick smart numbers. Let n=15 {why 15? Since cars=1/4*trucks, total trucks+cars should be divisible by 5 (1+4). Additionally since we have another fraction 2/3 to work with, the total should be divisible by 3} 
n=15 
cars+trucks= 15
cars+4*cars = 15 -> cars=3 so trucks=12
pick-up trucks = 12*2/3 = 8
Now plug 15 in answer choices. Only D gives 8. Ans D

gracie · Answer

let t=number of trucks
n=t+(t/4)=5t/4
let p=number of pickups
t=3p/2
substituting, n=5(3p/2)/4
p=8/15 n

santro789 · Answer

Number of trucks = x
Number of cars = 1/4x

Therefore, x +1/4x = n ( Total number of vehicles parked)
 X= 4n/5

We are given 2/3 of x are pick up trucks.
So 2/3 *4n/5 = 8/15n

shashankism · Answer

t+c = n 
c = t/4

t+t/4 = n 
t = 4/5 n

c = 2/3 t = 2/3 * 4/5 = 8/15 n

Answer D

ScottTargetTestPrep · Answer

We can let the number of cars = c and number of trucks = t; thus:

c + t = n

and

c = (1/4)t

Thus:

(1/4)t + t = n

t + 4t = 4n

5t = 4n

t = 4n/5

Since 2/3 of the trucks are pickups, there are (2/3)(4n/5) = 8n/15 pickups in the parking lot.

Answer: D

MathRevolution · Answer

Total: 'n = trucks(t) + cars(c)'

Number of cars is 1/4 the number of trucks: c =  \frac{1}{4}  * t

=> n =  \frac{1}{4}  * t + t =  \frac{5}{4}  * t  OR  t =  \frac{4}{5}  * n

\frac{2}{3}  of the trucks are pickups. Therefore,

=> t =  \frac{4}{5}  * n

=>  \frac{2}{3}  * t =  \frac{2}{3}  *  \frac{4}{5}  * n

=> Parked trucks:  \frac{8 }{ 15}  * n

Answer D

Kinshook · Answer

Given: A total of n trucks and cars are parked in a lot. 
Asked: If the number of cars is 1/4 the number of trucks, and 2/3 of the trucks are pickups, how many pickups, in terms of n, are parked in the lot?

Let the number of pickup trucks parked in the lot = x

Number of trucks = 3x/2
Number of cars = 3x/8

3x/2 + 3x/8 = n
15x/8 = n
x = 8n/15

IMO D

dave13 · Answer

what the difference between 1/4 the number vs 1/4 of the number ? any other similar twists when it comes to interpreting fractions

hi

chetan2u VeritasKarishma

chetan2u · Answer

Hi

Both mean the same mathematically, that is 1/4*number

ArnauG · Answer

Let's assume the number of trucks is represented by "t" and the number of cars is represented by "c."

According to the given information, the number of cars is 1/4 the number of trucks:

c = (1/4) * t

Next, it states that 2/3 of the trucks are pickups:

Pickup trucks = (2/3) * t

Now, we need to express the number of pickups in terms of "n," which represents the total number of trucks and cars in the lot.

Total number of vehicles = t + c

Since c = (1/4) * t, we can substitute this into the equation:

Total number of vehicles = t + (1/4) * t

Total number of vehicles = (5/4) * t

Since n represents the total number of vehicles, we can set up the equation:

n = (5/4) * t

Now, let's express the number of pickups in terms of "n":

Pickup trucks = (2/3) * t

Substituting the value of t from the equation n = (5/4) * t:

Pickup trucks = (2/3) *

Simplifying the expression:

Pickup trucks = (8/15) * n

Therefore, the number of pickups, in terms of n, parked in the lot is (8/15) n.

The correct answer is (D) 8/15 n.

karu26 · Answer

Let there be c cars and t trucks and p pickup trucks
n = t + c
t = 4c
hence, n = 5c
(2/3)t = p
p = (2/3)t = (2/3)(4c) = (8/3)c = (8/3)(n/5) = (8/15)n
hence answer is D

satish_sahoo · Answer

Trucks = T
Cars = C
 T+C=n

We have been given,  C= \frac{T}{4} 
So,  T + \frac{T}{4} = n 
 \frac{5T}{4 } = n

Now,
Pickups are  \frac{2}{3}  of T
So, Total pickups parked are
 \frac{2T}{3}/\frac{5T}{4}  =  \frac{8}{15}  of n

Answer D

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A total of n trucks and cars are parked in a lot. If the num

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