Question

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?

Answer 1

Rachel has 27

Hong has 51

Manuel has 17

Explanation:

Let R represent Rachel, H represent Hong, and M represent Manuel.

They combined have a total of 95. Thus:

`R+H+M=95`

Hong has 3 times what Manuel has. Therefore:

`H=3M`

Rachel has 10 more than Manuel. Therefore:

`R=10+M`

Substitute:

`R+H+M=95\\(10+M)+(3M)+M=95`

Combine like terms:

`5M+10=95`

Subtract 10 from both sides:

`5M=85`

Divide by 5:

`M=17`

Therefore, Manuel has 17.

Now, find Rachel and Hong's money.

`H=3M\\H=3(17)=51`

So, Hong has 51.

And for Rachel:

`R=10+M\\R=10+17=27`

Rachel has 27.