John, Karen, and Luke collected cans of vegetables for a food drive.

Question

John, Karen, and Luke collected cans of vegetables for a food drive. The number of cans that John collected was 1/2 the number of cans that Karen collected and 1/3 the number of cans that Luke collected. The number of cans that Luke collected was what fraction of the total number of cans that John, Karen, and Luke collected?

(A) 1/5
(B) 1/3
(C) 2/5
(D) 1/2
(E) 2/3

(A) 1/5
(B) 1/3
(C) 2/5
(D) 1/2
(E) 2/3

sashiim20 · Accepted Answer

John, Karen, and Luke collected cans of vegetables for a food drive. The number of cans that John collected was 1/2 the number of cans that Karen collected and 1/3 the number of cans that Luke collected. The number of cans that Luke collected was what fraction of the total number of cans that John, Karen, and Luke collected?

Let cans collected by John be X.
John collected \(\frac{1}{2}\) of the number of cans that Karen collected, ie; Karen's cans = 2X
John collected \(\frac{1}{3}\) of the number of cans that Luke collected, ie; Luke's cans = 3X
Total number of cans collected by Luke, John and Karen = X + 2X + 3X = 6X
Required fraction = Luke's cans/Total cans = \(\frac{3X}{6X}\) = \(\frac{1}{2}\)
Answer D...

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amanvermagmat · Answer

Assume number of cans John collected = 1
Then, number of cans Karen collected = 2
and number of cans Luke collected = 3

Total = 1+2+3=6

Cans with Luke as a fraction of total = 3/6 = 1/2

Hence  D

Kurtosis · Answer

John = (1/2)Karen --> Karen = 2(John)
John = 3(Luke) --> Luke = 3(John)

Total = 6(John)

Luke/Total = 3/6 = 1/2

Answer: D

pushpitkc · Answer

The best way is to find assume numbers and do the following problem

Given, number of cans of John was half the cans that Karen collected.
This number is also 1/3rd of the cans that Luke collection.
If 10 is the number of cans that John, collected.
Karen collected 20 cans and Luke, 30 cans.

Luke collected 30 out of total cans(10+20+30), which is 30/60 or 1/2(Option D)

ScottTargetTestPrep · Answer

We can create the equations:

J = K/2

2J = K

And

J = L/3

3J = L

So the fraction that Luke collected was:

L/(J + K + L) = 3J/(J + 2J + 3J) = 3J/6J = 1/2

Alternate Solution:

Let’s assume that John collected 5 cans. Since he collected half as many cans as Karen collected, then she collected 10 cans. Since John collected 1/3 the number of cans that Luke collected, then Luke collected 15 cans. Thus, the total number of cans collected was 5 + 10 + 15 = 30. So Luke collected 15/30 = ½ of all the cans collected.

Answer: D

user34745792203 · Answer

Number of collected cans can be written in the following way:

J : K : L

1 : 2 : 
1 : : 3

1 : 2 : 3

Luke: 3 
Total: 1+2+3

Ratio= 3/6 = 1/2

Hope it ́s clear!

AdarshSambare · Answer

Let cans collected by John be X.

Since John collected 1/2 the number of cans that Karen collected → Karen = 2X.
Since John collected 1/3 the number of cans that Luke collected → Luke = 3X.

Total cans = X + 2X + 3X = 6X.

Fraction = Luke / Total = 3X / 6X = 1/2.

Answer: D

John, Karen, and Luke collected cans of vegetables for a food drive.

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John, Karen, and Luke collected cans of vegetables for a food drive.

Prep Toolkit

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