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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?

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

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

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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.

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

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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