Answer:
Rachel has 27
Hong has 51
Manuel has 17
Step-by-step explanation:
Let R represent Rachel, H represent Hong, and M represent Manuel.
They combined have a total of 95. Thus:
[tex]R+H+M=95[/tex]
Hong has 3 times what Manuel has. Therefore:
[tex]H=3M[/tex]
Rachel has 10 more than Manuel. Therefore:
[tex]R=10+M[/tex]
Substitute:
[tex]R+H+M=95\\(10+M)+(3M)+M=95[/tex]
Combine like terms:
[tex]5M+10=95[/tex]
Subtract 10 from both sides:
[tex]5M=85[/tex]
Divide by 5:
[tex]M=17[/tex]
Therefore, Manuel has 17.
Now, find Rachel and Hong's money.
[tex]H=3M\\H=3(17)=51[/tex]
So, Hong has 51.
And for Rachel:
[tex]R=10+M\\R=10+17=27[/tex]
Rachel has 27.