Rachel, Hong, and Manuel have a total of 95 in their wallets. Hong has 3 times what Manuel has. Rachel has $10 more than Manuel. How much does each have?

Respuesta :

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.

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