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

Question

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

BrentGMATPrepNow · Accepted Answer

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:  E

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Harish Yannam · Answer

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

rhine29388 · Answer

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

dontgiveup2020 · Answer

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)

generis · Answer

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

Mo2men · Answer

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

ScottTargetTestPrep · Answer

Solution:

We can create the equations:

J + D + B = 72

and

J = 3B

J/3 = B

and

J = 3D/4

4J/3 = D

Substituting, we have:

J + 4J/3 + J/3 = 72

Multiplying by 3, we have:

3J + 4J + J = 216

8J = 216

J = 27

Thus D = 4(27)/3 = 36.

Answer: E

Abhishek009 · Answer

Let B = 3 , J = 9 and D = 12

Thus, 24 represents 72
Or, 1 represents 3
And 12 represents 36 , Answer must be (E)

akadiyan · Answer

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?

Total = 72

Lets consider money that Brad has = x

so josh has 3x

josh has $3x which is three-fourth as much as Doug, so doug has $4x

x+3x+4x=72
8x=72
x=9

Doug has $4x
substituting value of x , we get 4x = 4*9 = 36

Doug has $36

Ans:   E

CEdward · Answer

J + B + D = 72

J = 3B

J = 3D/4

3B + B + 4J/3 = 72 ---> 3B + B + 4B = 72 ---> B = 9

J = 3 x 9 = 27 = 3D / 4

D = 36

Answer is E.

adityasuresh · Answer

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 : B = 3 : 1
J : D =  3/4  : 1 ( Josh has three times as much money as Brad but only three-fourths as much as Doug)
(Multiply both sides by 4) J : D = 3 : 4
Combining ratios  J/B  =  3/1 ,  J/D  =  3/4 
J : B : D = 3 : 1 : 4
Therefore Doug's share = 4/8 * 72 = $36
 E

bumpbot · Answer

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

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