Distribute $399 among Peter, Betsy and Emma so that Betsy receives five times as much as Peter, and Emma receives three times as much as Betsy.
A) Peter receives $24, Betsy receives $120, Emma receives $255.
B) Emma receives $19, Betsy receives $95, Peter receives $285.
C) Betsy receives $19, Peter receives $95, Emma receives $285.
D) Peter receives $19, Betsy receives $95, Emma receives $285.
E) Emma receives $19, Peter receives $95, Betsy receives $285.

Question

Distribute $399 among Peter, Betsy and Emma so that Betsy receives five times as much as Peter, and Emma receives three times as much as Betsy.
A) Peter receives $24, Betsy receives $120, Emma receives $255.
B) Emma receives $19, Betsy receives $95, Peter receives $285.
C) Betsy receives $19, Peter receives $95, Emma receives $285.
D) Peter receives $19, Betsy receives $95, Emma receives $285.
E) Emma receives $19, Peter receives $95, Betsy receives $285.

Quizplus · Accepted Answer

Let the amount Peter receives be $x. 
Then, Betsy receives $5x (five times as much as Peter) and Emma receives $15x (three times as much as Betsy). 
We can set up the following equation: 
x + 5x + 15x = 399 
21x = 399 
x = 19 
Therefore, Peter receives $19, Betsy receives $95 (five times as much as Peter), and Emma receives $285 (three times as much as Betsy). 
Thus, the correct choice is D.

Distribute $399 Among Peter, Betsy and Emma So That Betsy