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

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:

$R+H+M=95$

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.