Maya, Henry, and Ryan have a total of $130 in their wallets. Ryan has $10 less than Maya. Henry has times what Ryan has. How much do they have in their wallets?

Question

I need dummy dumb talk here because I can't seem to get my equation right...

I know you make the equation - so this is what I have.

m+r-10+4h=130

I know I need to simplify so I want to get rid of the 10, right? So I add 10 to both sides?

m+r+4h=130? I don't think that's right? That's where my problem is...

Answer 1

Hi Helina,

Let's set up a relationship for each person the same way you did, where m= Maya's money, h= Henry's money, and r= Ryan's money.

The initial equation is as follows: m+h+r=130

Notice how, after the first sentence, Ryan is mentioned both times when talking about Henry or Maya. That means we can simplify the equation by focusing on Ryan's money, and his relationship to the others.

In your question, it says that "Ryan has $10 less than Maya". Another way of looking at this is saying "Maya has $10 more than Ryan". So now we have established a relationship between Ryan's money and Maya's money, where m= r+10

Your question stem also states that "Henry has 4 times what Ryan has" (I got the 4 from your equation, since the number is missing from the question stem). So now we have established a relationship between Henry's money and Ryan's money, where h=4*r, or h=4r

Now, we can plug in the two new equations we just made (m=r+10, and h=4r), into the initial equation from the beginning.

So now m+h+r=130 can be rewritten as r+10 + 4r +r = 130.

This new equation can be simplified to: 6r+10 = 130

So now we can subtract 10 from both sides to get 6r=120

And when we divide 120 by 6, that simplifies to r=20

So Ryan has $20. And we can use the equations we made earlier to find out how much money Maya and Henry has:

-For Maya: m=r+10, or in other words, m=20+10, m=30. So Maya has $30

-For Henry: h=4r, or in other words h= 4(20), h=80. So Henry has $80

So in summary, Ryan has $20, Maya has $30, and Henry has $80. And when we add these three numbers together, we get a total of $130.