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If Josh, Doug, and Brad have a total of $72 between them, and Josh has

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If Josh, Doug, and Brad have a total of $72 between them, and Josh has  [#permalink]

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New post 25 Aug 2016, 00:26
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E

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Question Stats:

83% (01:50) correct 17% (02:36) wrong based on 187 sessions

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If Josh, Doug, and Brad have a total of $72 between them, and Josh has three times as much money as Brad but only three-fourths as much as Doug, how much money does Doug have?

A. $8
B. $9
C. $27
D. $32
E. $36

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Re: If Josh, Doug, and Brad have a total of $72 between them, and Josh has  [#permalink]

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New post 25 Aug 2016, 06:32
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Bunuel wrote:
If Josh, Doug, and Brad have a total of $72 between them, and Josh has three times as much money as Brad but only three-fourths as much as Doug, how much money does Doug have?

A. $8
B. $9
C. $27
D. $32
E. $36


Lots of possible approaches here.
One approach is to TEST the answer choices to see which one satisfies the given information. I'll leave that one to you.

Another approach is to use some algebra.

Since both pieces of information reference Josh.....
Let J = the amount of money Josh has.

Josh has 3/4 as much money as Doug
Another way to say this is, "Doug has 4/3 as much money as Josh"
So, (4/3)J = the amount of money Doug has.

Josh has three times as much money as Brad
Another way to say this is, "Brad has 1/3 as much money as Josh"
So, (1/3)J = the amount of money Brad has.

Josh, Doug, and Brad have a total of $72 between them
So, we get: J + (4/3)J + (1/3)J = 72
Multiply both sides by 3 to get: 3J + 4J + J = 216
Simplify: 8J = 216
Solve: J = 27

Since (4/3)J = the amount of money Doug has, we can plug in 27 for J to get:
Doug's money = (4/3)(27) = 36

Answer:

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Re: If Josh, Doug, and Brad have a total of $72 between them, and Josh has  [#permalink]

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New post 25 Aug 2016, 07:39
Josh+Doug+Brad = 72 ; Joush = 3 brad, Josh =3/4 doug

Josh+1/3 Josh+ 4/3 Josh = 72 (substituted the given values)

Josh = 27. 27= 3/4 doug => doug =36 :)
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Re: If Josh, Doug, and Brad have a total of $72 between them, and Josh has  [#permalink]

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New post 21 Oct 2016, 02:41
consider the amount of money with Doug be $x
it is given Josh has \(\frac{3}{4}\) th amount of what Doug has , so Josh has \(\frac{3}{4}\) x

it is also given that amount with Josh is 3 times the amount with Brad
so Brad has (\(\frac{3x}{4}\))/3 = $ x/4

\(\frac{3x}{4}\) +\(\frac{x}{4}\) + x = 72

solving we get x = 36
so the amount with Doug is $ 36
correct answer - E
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Re: If Josh, Doug, and Brad have a total of $72 between them, and Josh has  [#permalink]

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New post 29 Dec 2017, 10:04
J + D + B = 72 (equation 1)
J = 3B (equation 2)
J = (3/4)D (equation 3)

Since we are looking for variable D, it will be faster to convert J and B in equation 1 to their equivalent amount in variable D.

We already know that J = (3/4)D and now just have to figure out B's equivalent in variable D.

Combining equations 2 and 3, we know that 3B = (3/4)D, hence B = (1/4)D (equation 4).

Substituting equation 2 and equation 4 into equation 1 gives us: (3/4)D + D + (1/4)D = 72.
Simplifying that gives us 2D = 72.
Hence, D = 36 (answer E)
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If Josh, Doug, and Brad have a total of $72 between them, and Josh has  [#permalink]

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New post 29 Dec 2017, 16:14
Bunuel wrote:
If Josh, Doug, and Brad have a total of $72 between them, and Josh has three times as much money as Brad but only three-fourths as much as Doug, how much money does Doug have?

A. $8
B. $9
C. $27
D. $32
E. $36

I used Brad, B, as the "base." This answer looks time-consuming. It isn't; I just laid out the steps.

\(B + J + D = 72\)

\(J = 3B\)

\(J = \frac{3}{4}D\)

\(\frac{4}{3}J =
(\frac{3}{4})*(\frac{4}{3})D\)

\(D =
\frac{4}{3}J\)

Substitute \(J = 3B\)
\(D= \frac{4}{3}*(3B) = 4B\)

\(B + 3B + 4B = 72\)
\(8B = 72\)
\(B = 9\)

\(D = 4B\)
\(D = 36\)


Answer E
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Re: If Josh, Doug, and Brad have a total of $72 between them, and Josh has  [#permalink]

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New post 29 Dec 2017, 16:51
Bunuel wrote:
If Josh, Doug, and Brad have a total of $72 between them, and Josh has three times as much money as Brad but only three-fourths as much as Doug, how much money does Doug have?

A. $8
B. $9
C. $27
D. $32
E. $36


J + D + B = 72

J = 3B & J =3/4 D...(This means that Doug's amount is great....so I think in choices C, D & E)

Pick choice D ( strategy between 2 answers) ...So we do not do many calculation

Doug =32

J = 3/4 * 32 = 24

B = 8

32 + 24 + 8 = 64..it means Doug has more than 32...........So we have only one answer left & no need to check

Answer: E
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Re: If Josh, Doug, and Brad have a total of $72 between them, and Josh has &nbs [#permalink] 29 Dec 2017, 16:51
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If Josh, Doug, and Brad have a total of $72 between them, and Josh has

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