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# Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot

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Math Expert
Joined: 02 Sep 2009
Posts: 51218
Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot  [#permalink]

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23 Feb 2016, 01:52
00:00

Difficulty:

5% (low)

Question Stats:

88% (02:28) correct 12% (03:11) wrong based on 136 sessions

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Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot dog eating contest. If Jim ate four times as many hot dogs as Leon but half as many hot dogs as Billy, how many more hot dogs did Billy eat than Leon?

A. 13
B. 20
C. 39
D. 42
E. 60

Kudos for correct solution.

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Math Expert
Joined: 02 Aug 2009
Posts: 7107
Re: Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot  [#permalink]

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23 Feb 2016, 09:12
2
Bunuel wrote:
Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot dog eating contest. If Jim ate four times as many hot dogs as Leon but half as many hot dogs as Billy, how many more hot dogs did Billy eat than Leon?

A. 13
B. 20
C. 39
D. 42
E. 60

Kudos for correct solution.

hi,
two ways you can tackle these problems, although the concept/logic is same--
1) ratio--
clearly ratio between B:J:L=8:4:1..
since J:L=4:1 and B:J=2:1..
let the common ratio be x, so total=13x and x=78/13=6..
difference in B and L= (8-1)x=7*6=42..
D

2) Equations..
L+B+J=78..
Jim ate four times as many hot dogs as Leon
J=4L..
Jim ate half as many hot dogs as Billy
J=B/2 or B=2J..
since L+B+J=78.. L+4L+2*4L=78..
L=78/13=6..
so B=2*4L=8*6=48..

ans 48-6=42..

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Joined: 07 Feb 2016
Posts: 6
Re: Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot  [#permalink]

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23 Feb 2016, 09:25
1
Since Leon has eaten the lowest number of htdgs, Let's consider,
the number of htdgs eaten by Leon= x
and htdgs etn by Jimmy=4x
And by Billy=2*4x=8x

Total number of htdgs= x+4x+8x = 13x

13x=78 => x=6

we need to find difference between Billy's and Leon's consumption, i.e. 8x-x = 7x

7*6=42

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Re: Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot  [#permalink]

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23 Feb 2016, 09:28
1
Bunuel wrote:
Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot dog eating contest. If Jim ate four times as many hot dogs as Leon but half as many hot dogs as Billy, how many more hot dogs did Billy eat than Leon?

A. 13
B. 20
C. 39
D. 42
E. 60

Kudos for correct solution.

Let $$l$$, $$b$$ and $$j$$ represent the number of hotdogs eaten by Leon, Billy and Jim, respectively.
Jim ate four times as many hot dogs as Leon.
so, $$j = 4l$$
But Jim ate half as many hot dogs as Billy
so, $$j = 1/2b$$
replace $$j = 4l$$ in the above equation. we get:
$$4l = 1/2b$$ or $$b = 8l$$

We know, $$j + l + b = 78$$
replace, $$j = 4l$$ and $$b = 8l$$ in the above equation, we get
$$4l + l + 8l = 78$$
This means, $$13l = 78$$ or $$l = 6$$
Leon ate 6 hotdogs.
$$b = 8l$$ = 8 x 6 = 48
Billy ate 48 hotdogs
How many more hot dogs did Billy eat than Leon?
= $$b - l$$ = 48 - 6 = 42
Hence, D is the correct answer.
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Re: Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot  [#permalink]

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23 Feb 2016, 11:52
1
L+b+j=78
J=4l -> l=j/4
J=b/2 -> b=2j

J/4+2j+j=78
13j= 78×4
J=24
B=48
L=6

B-l=42
Ans:D
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Posts: 3238
Re: Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot  [#permalink]

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23 Feb 2016, 15:51
1
Bunuel wrote:
Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot dog eating contest. If Jim ate four times as many hot dogs as Leon but half as many hot dogs as Billy, how many more hot dogs did Billy eat than Leon?

A. 13
B. 20
C. 39
D. 42
E. 60

Let x = # of hot dogs that Jim ate

Jim ate four times as many hot dogs as Leon
In other words, Leon ate 1/4 as many hot dogs as Jim ate
So, x/4 = # of hot dogs that Leon ate

Jim ate half as many hot dogs as Billy
In other words, Billy ate twice as many hot dogs as Jim ate
So, 2x = # of hot dogs that Billy ate

In TOTAL they ate 78 hot dogs
So, x + x/4 + 2x = 78
Solve to get: x = 24

So...
Jim ate 24 hot dogs
Leon ate 6 hot dogs
Billy ate 48 hot dogs

How many more hot dogs did Billy eat than Leon?
48 - 6 = 42 = D

Cheers,
Brent
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Posts: 3238
Re: Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot  [#permalink]

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23 Feb 2016, 15:52
1
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Cheers,
Brent
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Re: Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot  [#permalink]

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27 Feb 2018, 09:42
Bunuel wrote:
Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot dog eating contest. If Jim ate four times as many hot dogs as Leon but half as many hot dogs as Billy, how many more hot dogs did Billy eat than Leon?

A. 13
B. 20
C. 39
D. 42
E. 60

We can let the number of hot dogs eaten by Leon, Billy, and Jim = L, B, and J, respectively, and create the equations:

L + B + J = 78

and

J = 4L
J/4 = L

and

J = (1/2)B

2J = B

Substituting, we have:

J/4 + 2J + J = 78

J/4 + 3J = 78

Multiplying by 4 we have:

J + 12J = 312

13J = 312

J = 24

Thus, B = 2(24) = 48 and L = 24/4 = 6.

So Bill ate 48 - 6 = 42 more hot dogs than Leon.

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Re: Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot &nbs [#permalink] 27 Feb 2018, 09:42
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