Mark and Hayden won a raffle and decided to split the prize money using the ratio 9:8. if Hayden received $64, which of the following was the total amount of money that Mark and Hayden won?
1. $72
2. $80
3. $136
4. $170

Question

Mark and Hayden won a raffle and decided to split the prize money using the ratio 9:8. if Hayden received $64, which of the following was the total amount of money that Mark and Hayden won? 
1. $72 
2. $80 
3. $136 
4. $170

anonymous · Answer

@whpalmer4

anonymous · Answer

Mind helping again?:)

whpalmer4 · Answer

Sure, one more and then I have to do some other stuff away from the computer...

whpalmer4 · Answer

Okay, this is sort of like working the last problem in the other direction.

anonymous · Answer

I feel the answer is 72

whpalmer4 · Answer

Mark gets 9 and Hayden gets 8 out of each "batch".  But how many batches are there?  If we can figure that out, we can figure out how much the total was, and how much Mark won (not required by the problem).

whpalmer4 · Answer

Well, you have fallen into the dastardly trap set for you :-)

whpalmer4 · Answer

Let's think about this for a second.  Hayden got $64.  Mark gets a bit more than Hayden (9:8 ratio), and you think that $72 is going to be the total they won?  The problem asks " was the total amount of money that Mark and Hayden won? "

Here's a tip: whenever you think you have an answer, re-read the problem and ask yourself, "am I answering the question in the problem, or did I answer something else?"

anonymous · Answer

Sorry i read the question wrong I am thinking it would be 136 because 136-64 = 72 which is a bit more than Hayden got.

whpalmer4 · Answer

Well, if the money gets split 9:8, each "batch" of money is 17 dollars.  We also know that Hayden got 64 dollars, and his share of each "batch" is 8 dollars.  From that, we can figure out that there must be 64/8 = 8 batches, right?  And Mark is getting 9*8 = 72 dollars.

whpalmer4 · Answer

The answer we are looking for is 136 dollars for the total that they received.

We could also find the amount that Mark received (and then get the answer sought by the problem author) by using the ratio.  Mark gets 9:8 of the money Hayden gets.

We can write a ratio $a:b$ as $\dfrac{a}{b}$, so 

$$Mark = \frac{9}{8} Hayden$$
$$Mark = \frac{9}{8}*64 = 72$$

and again, total won = Mark + Hayden = 72+64 = 136 as you found.

anonymous · Answer

Thank u :) you are awesome

whpalmer4 · Answer

Glad I could help!  Another tip: if you really want to nail something down in your understanding, try explaining it to someone else.

anonymous · Answer

Ill keep that in mind thank you :)